   Chapter 3.1, Problem 31E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Differentiate the function. z = A y 10 + B e y

To determine

To find: The derivative of the function z=Ay10+Bey.

Explanation

Given:

The function, z=Ay10+Bey.

Formula used:

The Constant Multiple Rule:

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

ddy[cf(y)]=cddyf(y) (1)

The Power Rule:

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

ddy(yn)=nyn1 (2)

Derivative of the Natural Exponential Function:

ddy(ey)=ey (3)

The Sum Rule:

If f(y) and g(y) are both differentiable function, then the sum rule is,

ddy[f(y)+g(y)]=ddy(f(y))+ddy(g(y)) (4)

Calculation:

The derivative of z=Ay10+Bey is dzdy, which is obtained as follows:

dzdy=ddy(z) =ddy(Ay10+Bey)=ddy(Ay10+Bey)

Apply the sum rule as shown in equation (4)

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