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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Differentiate.

f ( t ) = cot t e t

To determine

To find: The differentiation of f(t)=cottet.

Explanation

Given:

The function is f(t)=cottet.

Formula used:

The Quotient Rule:

If f(t) and g(t) are differentiable functions, then the quotient rule is,

ddt[f(t)g(t)]=g(t)ddt[f(t)]f(t)ddt[g(t)][g(t)]2 (1)

Calculation:

Apply the quotient rule as shown in equation (1).

Substitute cott for f(t) and et for g(t) in equation (1).

ddt[cottet]=etddt[cott]cottddt[et]

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