   Chapter 11.3, Problem 31E ### 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 ln x = y 2 , find d y / d x .

To determine

To calculate: The value of dydx for the provided equation lnx=y2.

Explanation

Given Information:

The provided equation is, lnx=y2.

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 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,

dydx=dydududx

Calculation:

Consider the provided equation,

lnx=y2

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

ddx(lnx)=ddx(y2

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