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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

Differentiate the function.

G ( t ) = 5 t + 7 t

To determine

To find:  The derivative of the function G(t)=5t+7t.

Explanation

Given:

The function, G(t)=5t+7t.

Formula used:

The Constant Multiple Rule:

If c is a constant and f(x) is a differentiable function, then the constant multiple rule is,

ddx[cf(x)]=cddxf(x) (1)

The Power Rule:

If n is any real number, then the power rule is,

ddx(xn)=nxn1 (2)

The Sum Rule:

If f(x) and g(x) are both differentiable functions, then the sum rule is,

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

Calculation:

The derivative of G(t) is G(t), which is obtained as follows:

G(t)=ddt(5t+7t) =ddt(5t+7t1)=ddt(5t12+7t1) 

Apply the sum rule as shown in equation (3)

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