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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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Find the derivative of

f ( x ) = ln 5 x

To determine

To calculate: The derivative of the function f(x)=ln5x.

Explanation

Given information:

The provided function is f(x)=ln5x.

Formula used:

The chain rule of derivative for natural logarithm

ddxlnu=1ududx.

Where, u is the function of x.

The chain rule of derivative for power function:

ddx(un)=nun1dudx

Where, u is the function of x.

Calculation:

Consider the function f(x)=ln5x.

Let u=5x,

Now differentiate the function with respect to x.

dudx=ddx(5x)=5

Substitute, u for 5x in function,

f(x)=lnu

Now differentiate the function with respect to x

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