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Popular >

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

Solution

\frac{d}{d x} ((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

Popular Examples

(\partial)/(\partial x)(e^{8x+2y})

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\frac{d}{d x} (\frac{4 x}{( 2 x + 1 ) ^{2}})

integral of ((x^2+1))/(sqrt(x^3+3x))

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

(\partial)/(\partial x)(ln(x^6+y^4))

\frac{\partial}{\partial x} (ln (x^{6} + y^{4}))

derivative of sqrt(5+4x)derivative of

5 + 4 x

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