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Chapter 2: Q 16. (page 238)

Find the derivatives of the function:f(x)=exsinx.f(x)=exsinx.

Short Answer

Expert verified

The derivative of f(x)=exsinxisex{sinx-cosx}sin2x.

Step by step solution

01

Given information 

The given expression isf(x)=exsinx.

02

Simplification

f'(x)=ddxexsinx=sinxddx(ex)-exddx(sinx)sin2x=exsinx-excosxsin2x=ex{sinx-cosx}sin2xHence,f'(x)=ex{sinx-cosx}sin2x.

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Most popular questions from this chapter

Suppose h(t) represents the average height, in feet, of a person who is t years old.

(a) In real-world terms, what does h(12) represent and what are its units? What does h' (12) represent, and what are its units?

(b) Is h(12) positive or negative, and why? Is h'(12) positive or negative, and why?

(c) At approximately what value of t would h(t) have a maximum, and why? At approximately what value of t would h' (t) have a maximum, and why?

Find the derivatives of the functions in Exercises 21鈥�46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.

f(x)=x-12(x2-1)3

Find the derivatives of the functions in Exercises 21鈥�46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.

f(x)=3x-4(2x+1)6

Use (a) the h鈫�0definition of the derivative and then

(b) the z鈫�cdefinition of the derivative to find f'(c)for each function f and value x=c in Exercises 23鈥�38.

27.f(x)=1-x3,x=-1

Each graph in Exercises 31鈥�34 can be thought of as the associated slope function f' for some unknown function f. In each case sketch a possible graph of f.

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