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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

Find the derivative of the function.

f ( t ) 2 t 3

To determine

To find: The derivative of f(t)=2t3.

Explanation

Given:

The function is f(t)=2t3.

Result used:

The Chain Rule:

If h is differentiable at t and g is differentiable at h(t), then the composite function F=gh defined by F(x)=g(h(t)) is differentiable at t and F is given by the product,

F(t)=g(h(t))h(t) (1)

Power Rule:

If n is positive integer, then ddx(xn)=nxn1 (2)

Calculation:

Obtain the derivative of f(t).

f(t)=ddx(f(x))=ddx(2t3)

Let h(t)=t3 and g(u)=2u  where u=h(t).

Apply the chain rule as shown in equation (1),

f(t)=g(h(t))h(t) (3)

The derivative g(h(t)) is computed as follows,

g(h(t))=g(u)=ddu(g(u))=ddu(2u)

Use the de

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