   Chapter 8.4, Problem 51E ### 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 sin x + cos 2 y = 1                           ( π 6 , π 6 )

To determine

To calculate: The dydx and value of dydx at point (π6, π6) of the provided function sinx+cos2y=1.

Explanation

Given Information:

The provided function is sinx+cos2y=1 and provided point is (π6, π6).

Formula used:

Sine differentiation rule:

ddx[sinu]=cosududx

Cosine differentiation rule:

ddx[cosu]=sinududx

General power rule of differentiation:

ddx[xn]=nxn1

Calculation:

Consider the provided function:

sinx+cos2y=1

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

ddx[sinx+cos2y]=ddxddx[sinx]+ddx[cos2y]=ddx[cosx]+[sin2yddx[2y]]=cosx[sin2y2dydx]=0

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