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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

Calculate y'.

41. y = x + 1 ( 2 x ) 5 ( x + 3 ) 7

To determine

To calculate: The derivative of y.

Explanation

Given:

The function is y=x+1(2x)5(x+3)7.

Result used: Chain Rule

If y=f(u) and u=g(x) are both differentiable functions, then dydx=dydududx.

Calculation:

Consider y=x+1(2x)5(x+3)7.

Take natural logarithm on both sides,

lny=ln[x+1(2x)5(x+3)7]lny=ln(x+1)(2x)5ln(x+3)7            (lnab=lnalnb)lny=(ln(x+1)+ln(2x)5)ln(x+3)7  (lnab=lna+lnb)lny=12ln(x+1)+5ln(2x)7ln(x+3)        (lnab=blna)

Differentiate both sides with respect to x

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