   Chapter 4.5, Problem 53E ### 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. x 2 − 3 ln y + y 2 = 10

To determine

To calculate: The value of dydx for the equation x23lny+y2=10 using the implicit differentiation.

Explanation

Given information:

The provided equation is x23lny+y2=10.

Formula used:

Let u be a differentiable function of x then, ddx[lnx]=1x,x>0 and ddx(lnu)=1ududx,u>0

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 x23lny+y2=10,

Take ddx of both sides of the above equation,

ddx(x23lny+y2)=ddx(10)ddx(x2)ddx(3lny)+ddx(y2)=ddx(10)

Apply the logarithmic function rule of derivative in (lny) and the chain rule of derivative to the function x2 and y2,

(ddx(x2)dydx(3lny<

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