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Chapter 2: Q 28. (page 222)

Find the derivatives of the functions:f(x)=exe

Short Answer

Expert verified

The required answer isxe-1exe+1.

Step by step solution

01

Step 1. Given information.  

The given function isf(x)=exe.

02

Step 2. Find the derivative of the given function.

f(x)=exef'(x)=鈥�鈭�鈭�鈥�xexe=exeddx(xe)=exeexe-1=exe+1xe-1

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Most popular questions from this chapter

A bowling ball dropped from a height of 400feet will be s(t)=400-16t2feet from the ground after tseconds. Use a sequence of average velocities to estimate the instantaneous velocities described below:

After t=1 seconds, with h=0.5,h=0.25,h=-0.5andh=-0.2

Write down a rule for differentiating a composition f(u(v(w(x))))of four functions

(a) in 鈥減rime鈥� notation and

(b) in Leibniz notation.

Use the definition of the derivative to find f'for each function fin Exercises 34-59

f(x)=3x

A bowling ball dropped from a height of 400feet will be s(t)=400-16t2feet from the ground after tseconds. Use a sequence of average velocities to estimate the instantaneous velocities described below:

After t=2 seconds, with h=0.1,h=0.01h=-0.1andh=-0.01

Use the definition of the derivative to find ffor each function fin Exercises 39-54

f(x)=1x2-1
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