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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Differentiating Logarithmic Functions In Exercises 1-22, find the derivative of the function. See Examples 1, 2, 3, and 4.

y = e x 2 ln 4 x 3

To determine

To calculate: The derivative of the function y=ex2ln4x3.

Explanation

Given information:

The provided function is y=ex2ln4x3.

Formula used:

Let a be a positive real number a1 and u be a differentiable function of x. The derivative of natural logarithm of a function is,

ddx[logau]=(1lna)(1u)dudx

Product rule of derivative of differentiable functions, f(x) and g(x) is,

ddx[f(x)g(x)]=f(x)g(x)+f(x)g(x)

The derivative of function f(x)=un using the chain rule is,

f(x)=ddx(un)=nun1dudx

Where, u is the function of x

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