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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

Differentiate.

h ( r ) = a e r b + e r

To determine

To find: The differentiation of the function h(r)=aerb+er.

Explanation

Derivative rule:

(1) Quotient Rule: If f1(x) and f2(x) are both differentiable, then

ddx[f1(x)f2(x)]=f2(x)ddx[f1(x)]f1(x)ddx[f2(x)][f2(x)]2

(2) Power Rule: ddx(xn)=nxn1

(3) Sum rule: ddx(f+g)=ddx(f)+ddx(g)

(4) Constant multiple rule: ddx(cf)=cddx(f)

(5) Natural exponential function: ddx(ex)=ex

Calculation:

The derivative of the function h(r)=aerb+er is h(r), which is obtained as follows,

h(r)=ddr(aerb+er)

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

h(r)=(b+er)ddr(aer)(aer)ddr(b+er)(

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