Please solve problems Using L'hopital's Rule evaluate the following derivatives:5x3limx→0 7x + 32x-sin t2lim8x2limX→0COS x - 120 – T-lim0>T/2 COS (20)1 - sin 0lim0>T/21 + cos 20limx-o ln (sec x)t(1 – cos t)lim-→0 t - sin t-

If limx→x0 f(x)g(x) is of the 00 form then By L'Hospital rule limx→x0 f(x)g(x)=limx→x0 f'(x)g'(x)If…

Answered: Using L'hopital's Rule evaluate the…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.2: Derivatives Of Products And Quotients

Problem 35E

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Find the derivative: 2 y = ln² (3x + 1) O y K O y = = 0 y = O y = 2 ln(3x + 1) (3x + 1) 6 (3x + 1) 3 (3x + 1) 6 ln(3x + 1) (3x + 1)
6. Find the derivative of y= 2x² (3x - 4). A. 6x³ - 8x² B. 18x² - 16x 7. Find the derivative: f(x) = x sinx A. x\cosx - 4x3sinx B. x cosx + 4x³sinx C. 15x² - 6x D. 6x-4 C. 4x3cosx D. -4x³cosx
2. Computing Derivatives; Compute each derivative using the derivative rules: d cos-"(1+ x²) + tan (a) dx -'(1 + c*) e3x² d (b) (cos(1+x²) + tan'+e3=² da d (c) (1+ x² + ln[1 +x + sin¬'(1 + x)]) dx
The derivative of 01 COS I sin x esin(x) + ecos(x) et dt is - cos(x)esin(x) — sin(x)ecos(x) cos(x)esin(x) + sin(x)ecos(x) ecos(x) — esin(x)
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assume cos(t)=-1/4 where pi/2<t<pi cos(-t)= sin(t)= sin(-t)= sin(-t)+cos(-t)= sin^2(-t)+cos^2(-t)= sin(t-pi/2)= cos(t+pi/2)=
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Find the derivative of f(x) = (6x? + 6x – 4)arctan x a. (6x? + 6x – 4)*rctan x. arctan x 6x2+6x-4 b. (6x? + 6x - 4)arctan (In(6x? + 6x – 4) + arctan x- (12x + 6)) 1+x2 6x2+6x-4 c. (6x? + 6x – 4) In(arctan(x)), 12x+6 6x2+6x-4 + In(6x? + 6x – 4)- arctan x arctan x 1+x2 d. (6x? + 6x – 4)rctan x (In(arctan(x)) 12x + In(6x + 6x - 4)- 6x2+6x-4 1+arctan? x 1+x2 12x-4 e. (6x? + 6x – 4)arctan x (In(arctan(x))- + In(6x? + 6x – 4)- 6x2+6x-4 arctan x 1+x
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Obtain the derivative of Screen Shot 2021-10-05 at 9.01.21 AM.png y = (3 vx – x² + 2)x5 33 x/2 – 7x6 + 10x* 2 | 33 x7/2 – 7x6 + 10x4 2 27 -x7/2 2*² – 3x6 – 10x4 | 27 -x9/2 – 3x6 + 10x4 2 D

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Using L'hopital's Rule evaluate the following derivatives: 5x – 2x lim x→0 7x3 + 3 sin t2 lim 8x2 lim x0 COS x - 1