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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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Finding Derivatives Implicitly In Exercises 53-56, find dy/dx implicitly.

4 x 3 + ln y 2 + 2 y = 2 x

To determine

To calculate: The value of dydx for the equation 4x3+lny2+2y=2x using the implicit differentiation.

Explanation

Given information:

The provided equation is 4x3+lny2+2y=2x.

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,

4x3+lny2+2y=2x

Take ddx of both sides of the above equation,

ddx(4x3+lny2+2y)=ddx(2x)ddx(4x3)+ddx(lny2)+ddx(2y)=ddx(2x)

Apply the chain rule of derivative to the function 4x3 y2 2y, and 2x,

(ddx(4x3)+dydx(2lny)+dydx(2y))=dydx(2x)12<

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