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Chapter 2: Q 18. (page 222)

Find the derivatives of the functions:f(x)=log2(3x2-5)

Short Answer

Expert verified

The required answer is6xln2(3x2-5).

Step by step solution

01

 Step 1. Given information. 

The given function is:f(x)=log2(3x2-5)

02

Step 2. Find the derivative of the given function.

f(x)=log2(3x2-5)f(x)=ddxlog2(3x2-5)=1ln2(3x2-5)ddx(3x2-5)=1ln2(3x2-5)ddx(3x2)-ddx5=1ln2(3x2-5)(6x-0)=6xln2(3x2-5)

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Most popular questions from this chapter

Use the definition of the derivative to find the equations of the lines described in Exercises 59-64.

The line that passes through the point (3,2)and is parallel to the tangent line to f(x)=1x at x=-1.

Find a function that has the given derivative and value. In each case you can find the answer with an educated guess and check process it may be helpful to do some preliminary algebra

f'(x)=x(4-2x);f(0)=0

Differentiate f(x)=3x+x2in three ways. When you have completed all three parts, show that your three answers are the same:

(a) with the chain rule

(b) with the product rule but not the chain rule

(c) without the chain or product rules.

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.

28.f(x)=x4+1,x=2

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.

24.f(x)=x3,x=1
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