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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

Find the differential of each function.

11. (a) y = xe–4x

(b) y = 1 t 4

(a)

To determine

To find: The differential of the function.

Explanation

Given:

The function is y=xe4x.

Derivative rules:

(1) Chain rule: If y=f(u) and u=g(x)  are both differentiable function, then

dydx=dydududx.

(2) Product Rule: If f1(x) and f2(x) are both differentiable, then

ddx(f1(x)f2(x))=f1(x)ddx(f2(x))+f2(x)ddx(f1(x)).

Result used:

If y=f(x), then the differential is dy=f(x)dx.

Calculation:

The differential of the function is computed as follows,

Consider y=f(x).

Differentiate f(x)=xe4x with respect to x,

f(x)=ddx(xe4x)

Apply the product rule (2) and chain rule (1),

f(x)=xddx(e4

(b)

To determine

To find: The differential of the function.

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