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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

Find y″ if x6 + y6 = 1.

To determine

To find: The second derivative of x6+y6=1.

Explanation

Given:

The equation is x6+y6=1.

Derivative Rule:

Quotient Rule: ddx[fg]=gddx[f]fddx[g](g)2

Calculation:

The first derivative of x6+y6=1 is y, which is obtained as follows,

x6+y6=1

Differentiate implicitly on both sides with respect x,

ddx(x6+y6)=ddx(1)6x61+6y61dydx=06x5+6y5y=0y=x5y5

Thus, the first derivative of x6+y6=1 is y=x5y5.

The second derivative of x6+y6=1 is y, which is obtained as follows.

y=ddx(y) =ddx(x5y5) 

Apply the quotient rule (1) and simplify the terms,

y=(y5)ddx[x5](x5)d

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