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Chapter 2: Q 44. (page 222)

Find the derivatives of each of functions in Exercises 17鈥�44. In some cases it may be convenient to do some preliminary algebra.
fx=21-3x

Short Answer

Expert verified

The required answer is-3x路21-3x路In2路In3.

Step by step solution

01

Step 1. Given information.

The given function is:

fx=21-3x

02

Step 2. Find the derivative of the given function.

fx=21-3x

Differentiate the function,

f'x=ddx21-3x=-In2路21-3x路3xIn3=-3x路21-3x路In2路In3

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Most popular questions from this chapter

Suppose u(x)=3x2+1and f(u)=u2+3u51-u. Use the chain rule to find role="math" localid="1648356625815" ddx(f(u(x))) without first finding the formula for f(u(x)).

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(3x2+1)9

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)=1-4x2(3x2+1)9

Find the derivative of the absolute value function and piecewise defined function

f(x)=3x+1ifx鈮�1x3ifx>1

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.
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