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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 Functions of Other Bases In Exercises 107-112, find the derivative of the function.

y = log 10 3 x

To determine

To calculate: The derivative of the function y=log103x.

Explanation

Given Information:

The provided function is y=log103x.

Formula used:

If the function is f(x)=ln(ab), then the division property of logarithms is given by.

ln(ab)=ln(a)ln(b)

If the function is f(x)=[lnt], then the chain rule for logarithmic function is given by.

f(x)=1t.dtdx

Calculation:

Consider the function, y=log103x

Rewrite the expression by applying division property of logarithms.

y=ddx[log103x]=ddx[log10(3)log10(x)]

Evaluate the derivative by applying the chain rule of logarithms

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