   Chapter 11.3, Problem 33E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# If y 2 ln x = 4 , find d y / d x .

To determine

To calculate: The value of dydx for the provided equation y2lnx=4.

Explanation

Given Information:

The provided equation is:

y2lnx=4

Formula used:

When y is an implied function of x, obtain dydx by differentiating both sides of the equation with respect to x and then algebraically solve for dydx.

According to the product rule of derivatives:

ddx(uv)=udvdx+vdudx

According to the chain rule, if f and g are differentiable functions with y=f(u) and u=g(x), then y is a differentiable function of x and:

dydx=dydududx

Calculation:

Consider the provided equation:

y2lnx=4

First, take the derivative of both sides of the equation with respect to x as:

ddx(y2lnx)=ddx(4)

Now use the product rule of derivatives:

ddx(uv)=udvdx+vdudx

To obtain the derivative of y2lnx

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