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Popular >

derivative of (x+x^{-1})^3

Solution

derivative of

(x + x^{- 1})^{3}

Solution

3 x^{2} - \frac{3}{x ^{2}} - \frac{3}{x ^{4}} + 3

Solution steps

\frac{d}{d x} ((x + x^{- 1})^{3})

Apply the chain rule:

3 (x + x^{- 1})^{2} \frac{d}{d x} (x + x^{- 1})

= 3 (x + x^{- 1})^{2} \frac{d}{d x} (x + x^{- 1})

\frac{d}{d x} (x + x^{- 1}) = 1 - \frac{1}{x ^{2}}

= 3 (x + x^{- 1})^{2} (1 - \frac{1}{x ^{2}})

Simplify

3 (x + x^{- 1})^{2} (1 - \frac{1}{x ^{2}}) : 3 x^{2} - \frac{3}{x ^{2}} - \frac{3}{x ^{4}} + 3

= 3 x^{2} - \frac{3}{x ^{2}} - \frac{3}{x ^{4}} + 3

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\frac{d}{d x} (\frac{2}{1 - x ^{3}})

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\int x (3 x + 1) d x

sum from n=1 to infinity of cos^n(0.8)

n = 1 \sum \infty cos^{n} (0.8)

Frequently Asked Questions (FAQ)

What is the derivative of (x+x^{-1})^3 ?
The derivative of (x+x^{-1})^3 is 3x^2-3/(x^2)-3/(x^4)+3
What is the first derivative of (x+x^{-1})^3 ?
The first derivative of (x+x^{-1})^3 is 3x^2-3/(x^2)-3/(x^4)+3