   Chapter 11.2, Problem 3CP ### 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

# If s = t e t 2 , find ds/dt.

To determine

To calculate: The value of dsdt for the function s=tet2.

Explanation

Given Information:

The function is s=tet2.

Formula used:

If f(x)=cu(x), where, c is a constant and u(x) is a differentiable function of x, then,

f(x)=cu(x)

Where, u is a differentiable function of x,

According to the property of derivatives, if y=ex,

dydx=ex

According to the power rule of differentiation,

dydx=nxn1

According to the product rule of derivatives, for a function of type y=fg, the derivative is

dydx=fg+fg

Calculation:

Consider the function provided,

s=tet2

Differentiate both sides with respect to t,

dsdt=ddt(tet2)

Apply the product rule of derivatives,

dsdt

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