Find the derivative of the trigonometric function.g(t) = 3 cos² (πt)g'(t) = Find the derivative of the logarithmic function.h(x) = In(8x² + 5)h'(x)

Functions are given as and Note:Find:Derivatives of given functions.

Answered: Find the derivative of the…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Find the derivative of the trigonometric function.
g(t) = 3 cos² (πt)
g'(t) =

Find the derivative of the logarithmic function.
h(x) = In(8x² + 5)
h'(x)

Expert Solution

Step 1: Given data

Functions are given as

$g open parentheses t close parentheses equals 3 cos squared open parentheses pi t close parentheses$ and $h open parentheses x close parentheses equals ln open parentheses 8 x squared plus 5 close parentheses$

Note:

$fraction numerator d over denominator d x end fraction open square brackets cos open parentheses x close parentheses close square brackets equals negative sin open parentheses x close parentheses$

$fraction numerator d over denominator d x end fraction open parentheses x to the power of n close parentheses equals n x to the power of n minus 1 end exponent$

$fraction numerator d over denominator d x end fraction open parentheses ln open parentheses x close parentheses close parentheses equals 1 over x$

$fraction numerator d over denominator d x end fraction open parentheses alpha x close parentheses equals alpha$

$sin open parentheses 2 x close parentheses equals 2 sin open parentheses x close parentheses cos open parentheses x close parentheses$

Find:

Derivatives of given functions.

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