Q 8. Find the derivatives of the func... [FREE SOLUTION]

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Chapter 2: Q 8. (page 237)

Find the derivatives of the function: $f (x) = \frac{(x - 2)}{(x - 1) (x + 3)} .$

Short Answer

Expert verified

The derivative of $f (x) = \frac{(x - 2)}{(x - 1) (x + 3)} i s - \frac{(x^{2} - 4 x - 1)}{{(x^{2} + 2 x - 3)}^{2}} .$

Step by step solution

Given information

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

Simplification

$f' (x) = \frac{d}{d x} {\frac{(x - 2)}{(x - 1) (x + 3)}} = \frac{(x - 1) (x + 3) \frac{d}{d x} {(x - 2)} - (x - 2) \frac{d}{d x} {(x - 1) (x + 3)}}{{(x^{2} - x + 3 x - 3)}^{2}} = \frac{(x^{2} - x + 3 x - 3) . 1 - (x - 2) {1 . (x + 3) + 1 . (x - 1)}}{{(x^{2} + 2 x - 3)}^{2}} = \frac{x^{2} + 2 x - 3 - {(x - 2) 脳 (2 x + 2)}}{{(x^{2} + 2 x - 3)}^{2}} = \frac{x^{2} + 2 x - 3 - 2 x^{2} + 2 x + 4}{{(x^{2} + 2 x - 3)}^{2}} = - \frac{(x^{2} - 4 x - 1)}{{(x^{2} + 2 x - 3)}^{2}} H e n c e, \frac{d}{d x} {f (x)} = - \frac{(x^{2} - 4 x - 1)}{{(x^{2} + 2 x - 3)}^{2}} .$

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91影视

Find the derivatives of the function: $f (x) = \frac{(x - 2)}{(x - 1) (x + 3)} .$

Short Answer

Step by step solution

Given information

Simplification

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91影视

Find the derivatives of the function:f(x)=(x-2)(x-1)(x+3).

Short Answer

Step by step solution

Given information

Simplification

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Theoretical and Mathematical Physics

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Calculus

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Mechanics Maths

Study anywhere. Anytime. Across all devices.

Find the derivatives of the function: $f (x) = \frac{(x - 2)}{(x - 1) (x + 3)} .$