   Chapter 11.2, Problem 27E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Find the derivatives of the functions in Problems 1-34. y = 1 + e 5 x e 3 x

To determine

To calculate: The derivative of function, y=1+e5xe3x.

Explanation

Given Information:

The function provided is y=1+e5xe3x.

Formula used:

According to the property of derivatives, if f(x)=cu(x), where, c is a constant and u(x) is a differentiable function of x, then,

f(x)=cu(x)

According to the property of derivatives, for a function, y=eu, where, u is a differentiable function of x,

dydx=eududx

According to the quotient rule, for a function of form, y=fg, the derivative is

ddx(fg)=gffgg2

According to the power rule, if y=xn, then,

dydx=nxn1

If y=ex where, u is a differentiable function of x,

dydx=ex

Calculation:

Consider the function provided,

y=1+e5xe3x

Apply the quotient rule and differentiate both sides with respect to x,

dydx=ddx(1+e5xe3x)=e3xddx(1+e5x)(1+e5x)ddx(e3x)(e

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