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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 the function.

y = ex + 1 + 1

To determine

To find: The derivative of the function y=ex+1+1.

Explanation

Given:

The function, y=ex+1+1.

Formula used:

Derivative of a Constant Function:

If c is a constant function, then ddx(c)=0 (1)

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) (2)

Derivative of the Natural Exponential Function:

ddx(ex)=ex (3)

The Sum Rule:

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

ddx[f(x)+g(x)]=ddx(f(x))+ddx(g(x)) (4)

Calculation:

The derivative of y=ex+1+1 is dydx as follows:

dydx=ddx(y) 

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