   Chapter 4.5, Problem 54E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Finding Derivatives Implicitly In Exercises 53-56, find d y / d x implicitly. ln x y + 5 x = 30

To determine

To calculate: The value of dydx for the equation lnxy+5x=30 using the implicit differentiation.

Explanation

Given information:

The provided equation is lnxy+5x=30.

Formula used:

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.

Calculation:

Consider the equation, lnxy+5x=30

Take ddx of both sides of the above equation,

ddx(lnxy+5x)=ddx(30)ddx(lnxy)+ddx(5x)=ddx(30)

Apply logarithmic property to the provided equations,

ddx(lnx+lny)+ddx(5x)=ddx(30)

Apply the logarithmic function of derivative to the func

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