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Mathematical Applications for the ...

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

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Section
BuyFindarrow_forward

Mathematical Applications for the ...

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

If ln ( x + y ) = y 2 find d y / d x .

To determine

To calculate: The value of dydx for the provided equation ln(x+y)=y2.

Explanation

Given Information:

The provided equation is, ln(x+y)=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,

ln(x+y)=y2

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

ddx(ln(x+y))=ddx(y2)

Now, use the chain rule of derivatives,

dydx=dydududx

To obtain the derivatives of ln(x+y)a

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Chapter 11 Solutions

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