   Chapter 8.4, Problem 52E ### 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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# Implicit Differentiation In Exercises 51 and 52, use implicit differentiation to find d y / d x and evaluate the derivative at the given point.Equation Point 52. tan ( x + y ) = x                         ( 0 , 0 )

To determine

To calculate: The dydx and value of dydx at point (0, 0) of the provided function tan(x+y)=x.

Explanation

Given Information:

The provided function is tan(x+y)=x and provided point is (0, 0).

Formula used:

Tangent differentiation rule:

ddx[tanu]=sec2ududx

General power rule of differentiation:

ddx[xn]=nxn1

Calculation:

Consider the provided function:

tan(x+y)=x

Differentiate the above function using Sine, cosine and general power rules of differentiation.

ddx[tan(x+y)]=ddx[x]sec2(x+y)ddx(x+y)=1sec2(x+y)(1+dydx)=1sec2(x+y)+sec2(x+y)(dydx)=1

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