Fluent Essays

2021/9/18 下午10:05 2.3 Differentiation Formulas - Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign https://www.webassign.net/web/Student/Assignment-Responses/last?dep=27128647 1/20 EN Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 2.3 Di�erentiation Formulas (Homework) Current Score QUESTION POINTS TOTAL SCORE –/49 0.0% MON, SEP 20, 2021 4:00 PM PDT Request Extension Assignment Submission & Scoring Assignment Submission For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer. Assignment Scoring Your last submission is used for your score. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Home My Assignments Grades Communication Calendar My eBooks –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/2 –/2 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/2 Due Date https://www.cengage.com/dashboard/?ssoToken=8A85579F091539AF0500439A18DE5CC5FD139B72915C77A86851863DB62051E5FCBEDC930183D1B4A100666028C787732871B068C221DF7AAE99DEF58FF65A34D3A62510FA28CDD9&token=8A85579F091539AF0500439A18DE5CC5FD139B72915C77A86851863DB62051E5FCBEDC930183D1B4A100666028C787732871B068C221DF7AAE99DEF58FF65A34D3A62510FA28CDD9 https://www.webassign.net/manual/student_guide/ https://www.webassign.net/web/User/Cengage/my_account https://www.webassign.net/v4cgi/student.pl 2021/9/18 下午10:05 2.3 Differentiation Formulas - Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign https://www.webassign.net/web/Student/Assignment-Responses/last?dep=27128647 2/20 Differentiate the function. Differentiate the function. Differentiate the function. g(t) = 7t + 9t2 g ′(t) = g(x) = x − 2x + 11 9 4 2 g ′(x) = V(t) = t + t−3 ⁄ 5 5 V ′(t) = 1. [–/1 Points] SCALC9 2.3.002.DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 2. [–/1 Points] SCALC9 2.3.004.MI.DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 3. [–/1 Points] SCALC9 2.3.008.DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER javascript:open_bc_enhanced('master_it_alt',%20'/v4cgi/questions/tutorial_popup.tpl?struct=ABAuCsDRDODDEWDLAREtAREXEiCmDtAwBcCbAHADAdBHDnDiCMDUApBfAbDnDUDgEfDnBEDfBwBXCxCxEqAyACDIAcCVCXABCcAhANENEyAQCiDjCOAABjDbAiEXByEDBHBABfDLApEdEyAgEcBhChwWBhBLApAREQBKCcDpBVAgEIAaBgDfEVEGDaEVDXAQDfAwApCICxCqBFDEEFDoAEBqEHCdAMCoAACAERCaEfBnDCCdDFDJCaAPCCDkEyAvDDCWAXAmAgDLEPDnCCEaEmCRDKDCEnDUArETEREACyEgBfAWAPDSDtEWDGDKERDbBFBtCQEfCwADAuEkEqBWBsBKEhAgCwEcEBDWDEADCBAgCLAODDCPAfCIBIDMDwCjEvDSCXBtAyANDvAhDWCKAYBPDGCyuUDw&UserPass=c32844ea290fa05e11c5dedd7a5c8319&current=0&all=0') 2021/9/18 下午10:05 2.3 Differentiation Formulas - Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign https://www.webassign.net/web/Student/Assignment-Responses/last?dep=27128647 3/20 Differentiate the function. Differentiate the function. Differentiate the function after first rewriting the function in a different form. (Do not use the product or quotient rules.) h(w) = w − 6 6 h ′(w) = S(R) = 9 R2 S'(R) = F(t) = (5t − 4)2 F ′(t) = 4. [–/1 Points] SCALC9 2.3.012.DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 5. [–/1 Points] SCALC9 2.3.014.DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 6. [–/1 Points] SCALC9 2.3.016.DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER javascript:open_bc_enhanced('watch_it',%20'https://college.cengage.com/geyser/cengage_9780538738101/html/watchit_player/?asset=scalcet6_03_01_013&prod=scalcet6',%201) javascript:open_bc_enhanced('watch_it',%20'https://college.cengage.com/geyser/cengage_9780538738101/html/watchit_player/?asset=scalcet8_03_01_015&prod=scalcet8',%201) 2021/9/18 下午10:05 2.3 Differentiation Formulas - Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign https://www.webassign.net/web/Student/Assignment-Responses/last?dep=27128647 4/20 Differentiate the function after first rewriting the function in a different form. (Do not use the product or quotient rules.) Differentiate the function after first rewriting the function in a different form. (Do not use the product or quotient rules.) = y = 7 + 7x 2x x 2 y ′ = G(t) = + 6t t 3 G ′(t) 7. [–/1 Points] SCALC9 2.3.018.DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 8. [–/1 Points] SCALC9 2.3.020.DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 2021/9/18 下午10:05 2.3 Differentiation Formulas - Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign https://www.webassign.net/web/Student/Assignment-Responses/last?dep=27128647 5/20 Differentiate the function after first rewriting the function in a different form. (Do not use the product or quotient rules.) Consider the following. Find Find F(z) = A + Bz + Cz z 2 2 F ′(z) = y = + t x8 x t . dy dx = dy dx . dy dt = dy dt 9. [–/1 Points] SCALC9 2.3.022.DETAILS MY NOTES ASK YOUR TEACHER 10. [–/2 Points] SCALC9 2.3.026.DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 2021/9/18 下午10:05 2.3 Differentiation Formulas - Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign https://www.webassign.net/web/Student/Assignment-Responses/last?dep=27128647 6/20 Find the derivative of the function in two ways: by using the Quotient Rule and by simplifying first. (Check that your answers are equivalent. Which method do you prefer?) Quotient Rule = simplify first = Use the quotient rule to find the derivative of the function. F(x) = x − 7x + x 4 3 x 2 F ′(x) F ′(x) G(u) = 5u − 4u u + 1 4 G ′(u) = 11. [–/2 Points] SCALC9 2.3.028.DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 12. [–/1 Points] SCALC9 2.3.036.DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 2021/9/18 下午10:05 2.3 Differentiation Formulas - Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign https://www.webassign.net/web/Student/Assignment-Responses/last?dep=27128647 7/20 Differentiate. Differentiate. F(x) = 1 3x − 8x + 93 2 F ′(x) = y = + 7 x x y′ = 13. [–/1 Points] SCALC9 2.3.038.DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 14. [–/1 Points] SCALC9 2.3.040.DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 2021/9/18 下午10:05 2.3 Differentiation Formulas - Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign https://www.webassign.net/web/Student/Assignment-Responses/last?dep=27128647 8/20 Differentiate. Differentiate. Differentiate. h(w) = (w + 6w )(w − w )5 4 −4 −6 h ′(w) = F(t) = At Bt + Ct 2 6 9 F ′(t) = f(x) = ax + b cx + d f '(x) = 15. [–/1 Points] SCALC9 2.3.046.DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 16. [–/1 Points] SCALC9 2.3.050.DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 17. [–/1 Points] SCALC9 2.3.052.DETAILS MY NOTES ASK YOUR TEACHER 2021/9/18 下午10:05 2.3 Differentiation Formulas - Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign https://www.webassign.net/web/Student/Assignment-Responses/last?dep=27128647 9/20 Find an equation of the tangent line to the curve at the given point. Consider the following. Find an equation of the tangent line. y = Find an equation of the normal line. y = y = 3x − x + 6, (2, 26)3 2 y = y = x , (1, 1)5 ⁄ 4 18. [–/1 Points] SCALC9 2.3.060.DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 19. [–/2 Points] SCALC9 2.3.062.DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER javascript:open_bc_enhanced('watch_it',%20'https://college.cengage.com/geyser/cengage_9780538738101/html/watchit_player/?asset=scalcet8_03_01_033&prod=scalcet8',%201) 2021/9/18 下午10:05 2.3 Differentiation Formulas - Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign https://www.webassign.net/web/Student/Assignment-Responses/last?dep=27128647 10/20 Find equations of the tangent line and normal line to the curve at the specified point. tangent y = normal y = y = , 1, 0.2 x + 4 x 20. [–/2 Points] SCALC9 2.3.064.DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 2021/9/18 下午10:05 2.3 Differentiation Formulas - Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign https://www.webassign.net/web/Student/Assignment-Responses/last?dep=27128647 11/20 A graphing calculator is recommended. The graph of the function is called a serpentine. (a) Find an equation of the tangent line to this curve at the point (b) Illustrate part (a) by graphing the curve and the tangent line on the same screen. f(x) = x 1 + x2 (3, 0.30). y = ℹ ℹ 21. [–/2 Points] SCALC9 2.3.066.DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 2021/9/18 下午10:05 2.3 Differentiation Formulas - Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign https://www.webassign.net/web/Student/Assignment-Responses/last?dep=27128647 12/20 Find the first and second derivative of the function. = = ℹ ℹ G(r) = + r r 7 G'(r) G''(r) 22. [–/2 Points] SCALC9 2.3.068.DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER javascript:open_bc_enhanced('watch_it',%20'https://college.cengage.com/geyser/cengage_9780538738101/html/watchit_player/?rss=scalccc4_03_02_034&prod=scalccc4',%201) javascript:open_bc_enhanced('watch_it',%20'https://college.cengage.com/geyser/cengage_9780538738101/html/watchit_player/?asset=scalccc4_03_01_042&prod=scalccc4',%201) 2021/9/18 下午10:05 2.3 Differentiation Formulas - Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign https://www.webassign.net/web/Student/Assignment-Responses/last?dep=27128647 13/20 The equation of motion of a particle is where s is in meters and t is in seconds. (Assume t ≥ 0.) (a) Find the velocity, v(t), and acceleration, a(t), as functions of t. v(t) = a(t) = (b) Find the acceleration (in m/s ) after 1.3 s. (c) Graph the position, velocity, and acceleration functions on the same screen. s = t − 4t + t − t,4 3 2 2 a(1.3) = m/s2 23. [–/4 Points] SCALC9 2.3.074.DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 2021/9/18 下午10:05 2.3 Differentiation Formulas - Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign https://www.webassign.net/web/Student/Assignment-Responses/last?dep=27128647 14/20 ℹ ℹ 2021/9/18 下午10:05 2.3 Differentiation Formulas - Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign https://www.webassign.net/web/Student/Assignment-Responses/last?dep=27128647 15/20 ℹ ℹ 2021/9/18 下午10:05 2.3 Differentiation Formulas - Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign https://www.webassign.net/web/Student/Assignment-Responses/last?dep=27128647 16/20 The number of tree species S in a given area A in a forest reserve has been modeled by the power function where A is measured in square meters. Find (Round your answer to five decimal places.) Interpret your answer. The rate of change of the number of tree species with respect to area is 0.35599 species/m . The rate of change of the number of tree species with respect to area is −44.39254 species/m . The rate of change of the number of tree species with respect to area is −0.35599 species/m . The rate of change of the number of tree species with respect to area is 44.39254 species/m . The rate of change of the number of tree species with respect to area is 44.03655 species/m . Suppose that and Find (a) (b) (c) (d) S(A) = 0.882A0.842 S'(105). S'(105) = species/m2 2 2 2 2 2 f(4) = 4, g(4) = 5, f ′(4) = −3, g ′(4) = 2. h ′(4). h(x) = 2f(x) + 3g(x) h ′(4) = h(x) = f(x)g(x) h ′(4) = h(x) = f(x) g(x) h ′(4) = h(x) = g(x) f(x) + g(x) h ′(4) = 24. [–/2 Points] SCALC9 2.3.076.DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 25. [–/4 Points] SCALC9 2.3.080.DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 2021/9/18 下午10:05 2.3 Differentiation Formulas - Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign https://www.webassign.net/web/Student/Assignment-Responses/last?dep=27128647 17/20 If find Let and where F and G are the functions whose graphs are shown. (a) Find (b) Find h(2) = 3 and h'(2) = −7, . d dx h(x) x x = 2 P(x) = F(x)G(x) Q(x) = , F(x) G(x) ℹ P'(2). Q'(7). 26. [–/1 Points] SCALC9 2.3.082.DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 27. [–/2 Points] SCALC9 2.3.084.DETAILS MY NOTES ASK YOUR TEACHER 2021/9/18 下午10:05 2.3 Differentiation Formulas - Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign https://www.webassign.net/web/Student/Assignment-Responses/last?dep=27128647 18/20 If f is a differentiable function, find an expression for the derivative of each of the following functions. (a) (b) (c) (d) y = x f(x)6 y' = x f '(x) + 6x f(x)6 5 y' = x f '(x) − 5x f(x)5 6 y' = x f(x) − 6x f '(x)6 5 y' = x f(x) + 6x f '(x)6 5 y' = x f '(x) + 5x f(x)5 6 y = f(x) x5 y' = xf '(x) + 4f(x) x5 y' = xf(x) + 5f '(x) x5 y' = xf '(x) − 5f(x) x6 y' = xf '(x) − 4f(x) x6 y' = xf(x) − 5f '(x) x4 y = x f(x) 4 y' = f '(x)(3x ) − x f '(x) [f(x)] 3 4 2 y' = f '(x)(4x ) − x f(x) [f(x)] 3 4 2 y' = f '(x)(3x ) + x f(x) [f(x)] 4 3 2 y' = f(x)(3x ) + x f '(x) [f(x)] 4 4 2 y' = f(x)(4x ) − x f '(x) [f(x)] 3 4 2 y = 7 + xf(x) x y' = xf(x) + 7x f(x) − 2 2x 2 3/2 y' = xf '(x) − 2x f '(x) + 7 2x 2 3/2 28. [–/4 Points] SCALC9 2.3.086.DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 2021/9/18 下午10:05 2.3 Differentiation Formulas - Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign https://www.webassign.net/web/Student/Assignment-Responses/last?dep=27128647 19/20 For what values of x does the graph of f(x) have a horizontal tangent? (Enter your answers as a comma-separated list.) Find equations of the tangent lines to the curve that are parallel to the line (Enter your answers as a comma-separated list of equations.) y' = xf '(x) + 7x f(x) − 2 2x 2 3/2 y' = xf(x) + 2x f '(x) − 7 2x 2 3/2 y' = xf(x) − 7x f '(x) + 7 2x 2 3/2 f(x) = x + 3x + x + 73 2 x = y = x − 1 x + 1 x − 2y = 5. 29. [–/1 Points] SCALC9 2.3.088.MI.DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 30. [–/1 Points] SCALC9 2.3.092.DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER javascript:open_bc_enhanced('master_it_alt',%20'/v4cgi/questions/tutorial_popup.tpl?struct=AMARDREsBwCPBkBGBjBdAjENCeCrvVCKEPBTABCeDACGCuAvDFCDEJDJBqEQBCEDAWDmDHAUAGErDQBNBvEvChANCSETATwWEjDfEYDoDLArCjBWAqEICUDYCoEhCiEsAwBpyYDlChACAPBXExAJDyDLDxCHApCJEEDABVEmEdCVDoBeClBjAIDsCsCnBQzZEABNCABoEDDsCTBlBXDEDDCyAwCOAsBmDDCDDrCtEOEMDTCmETEyAqCMBVCHEQEsAOBoAkDmCdCgAaDkEEAvBUCgBnBkBtEFDOASCADPDfvVDLDsCdDYEeAtATDUCRBcEoAmCMAWyYEgAWAADNCXAvESCvEUEoDgAnEjAeCmCPAcAYDyEgERDmEHCKAhDJEfAEENCwEGDvzUBtEABxCsCiAuCXCDBNEl&UserPass=c32844ea290fa05e11c5dedd7a5c8319&current=0&all=0') 2021/9/18 下午10:05 2.3 Differentiation Formulas - Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign https://www.webassign.net/web/Student/Assignment-Responses/last?dep=27128647 20/20 Find equations of both lines through the point (2, −3) that are tangent to the parabola smaller slope y = larger slope y = Home My Assignments Request Extension Copyright © 1998 - 2021 Cengage Learning, Inc. All Rights Reserved TERMS OF USE PRIVACY y = x + x.2 Submit Assignment Save Assignment Progress 31. [–/2 Points] SCALC9 2.3.096.DETAILS MY NOTES ASK YOUR TEACHER https://www.cengage.com/legal/#terms https://www.cengage.com/privacy/