Q. 58 Use the differentiation rules de... [FREE SOLUTION]

Chapter 2: Q. 58 (page 198)

Use the differentiation rules developed in this section to find the derivatives of the functions in Exercises 35-64. Note that it may be necessary to do some preliminary algebra before differentiating.
$f (x) = \frac{x^{2} - 3 x}{x^{2} - 2 x + 1}$

Short Answer

Expert verified

The derivative of the function is $\frac{(2 x - 3) (x^{2} - 2 x + 1) - (x^{2} - 3 x) (2 x - 2)}{{(x^{2} - 2 x + 1)}^{2}}$ .

Step by step solution

Step 1. Given Information

The given function is $f (x) = \frac{x^{2} - 3 x}{x^{2} - 2 x + 1}$ .

Step 2. Find the derivative.

Apply the quotient rule of derivatives, $(\frac{f}{g})' (x) = \frac{f' (x) g (x) - f (x) g' (x)}{(g {(x))}^{2}}$ .

role="math" localid="1648660615294" $\begin{array}{rcl} f' (x) & = & \frac{\frac{d}{d x} (x^{2} - 3 x) 脳 (x^{2} - 2 x + 1) - (x^{2} - 3 x) \frac{d}{d x} (x^{2} - 2 x + 1)}{{(x^{2} - 2 x + 1)}^{2}} \\ = & \frac{(2 x - 3) (x^{2} - 2 x + 1) - (x^{2} - 3 x) (2 x - 2)}{{(x^{2} - 2 x + 1)}^{2}} \end{array}$

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Use the differentiation rules developed in this section to find the derivatives of the functions in Exercises 35-64. Note that it may be necessary to do some preliminary algebra before differentiating.
$f (x) = \frac{x^{2} - 3 x}{x^{2} - 2 x + 1}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find the derivative.

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91影视

Use the differentiation rules developed in this section to find the derivatives of the functions in Exercises 35-64. Note that it may be necessary to do some preliminary algebra before differentiating. f(x)=x2-3xx2-2x+1

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find the derivative.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Geometry

Statistics

Pure Maths

Mechanics Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Use the differentiation rules developed in this section to find the derivatives of the functions in Exercises 35-64. Note that it may be necessary to do some preliminary algebra before differentiating.
$f (x) = \frac{x^{2} - 3 x}{x^{2} - 2 x + 1}$