Q 7. Find the derivatives of the func... [FREE SOLUTION]

Chapter 2: Q 7. (page 237)

Find the derivatives of the function: $f (x) = \frac{1}{x^{4} - 5 x^{3} + 2} .$

Short Answer

Expert verified

The derivative of $f (x) = \frac{1}{x^{4} - 5 x^{3} + 2} i s - \frac{4 x^{3} - 15 x^{2}}{{(x^{4} - 5 x^{3} + 2)}^{2}}$ .

Step by step solution

Given information

The given expression is $f (x) = \frac{1}{x^{4} - 5 x^{3} + 2} .$

Simplification

$f' (x) = \frac{d}{d x} (f (x)) = \frac{d}{d x} (\frac{1}{x^{4} - 5 x^{3} + 2}) = - \frac{1}{{(x^{4} - 5 x^{3} + 2)}^{2}} . \frac{d}{d x} (x^{4} - 5 x^{3} + 2) = - \frac{4 x^{3} - 15 x^{2}}{{(x^{4} - 5 x^{3} + 2)}^{2}} = \frac{15 x^{2} - 4 x^{3}}{{(x^{4} - 5 x^{3} + 2)}^{2}} H e n c e, f' (x) = \frac{15 x^{2} - 4 x^{3}}{{(x^{4} - 5 x^{3} + 2)}^{2}} .$

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Find the derivatives of the function: $f (x) = \frac{1}{x^{4} - 5 x^{3} + 2} .$

Short Answer

Step by step solution

Given information

Simplification

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91影视

Find the derivatives of the function:f(x)=1x4-5x3+2.

Short Answer

Step by step solution

Given information

Simplification

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Most popular questions from this chapter

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Find the derivatives of the function: $f (x) = \frac{1}{x^{4} - 5 x^{3} + 2} .$