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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Differentiate.

y = c cos t + t2 sin t

To determine

To find: The differentiation of y=ccost+t2sint.

Explanation

Given:

The function is y=ccost+t2sint.

Formula used:

The Product Rule:

If f1(t) and f2(t) are both differentiable functions, then the product rule is,

ddt[f1(t)f2(t)]=f1(t)ddt[f2(t)]+f2(t)ddt[f1(t)] (1)

The Power Rule:

If n is real number, then the power rule is ddt(tn)=ntn1 (2)

The Sum Rule:

If f(x). and g(x) are both differentiations, then the summation rule is,

ddx[f(x)+g(x)]=ddx[f(x)]+ddx[g(x)] (3)

The Constant Multiple Rule:

If c is a constant and f(t) is differentiation function, then the constant multiple rule is,

ddt[cf(t)]=cddt[f(t)] (4)

Calculation:

Apply the sum rule as shown in equation (3).

ddt[ccost+t2sint]=ddt[ccost]+ddt[t2sint] (5)

Apply the constant multiple rule as shown in equation (4).

ddt[ccost]=cddt[cost]=csint

Apply the product rule as shown in equation (1)

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