What is the derivative of h(x)=(x+x^{-1})^3 ?

The derivative of h(x)=(x+x^{-1})^3 is 3x^2-3/(x^2)-3/(x^4)+3

What is the first derivative of h(x)=(x+x^{-1})^3 ?

The first derivative of h(x)=(x+x^{-1})^3 is 3x^2-3/(x^2)-3/(x^4)+3

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derivative of

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

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

\int e^{4 x + 9} d x

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f (x) = sin (cos (7 x))

\frac{d}{d x} (cosh^{4} (x))

\frac{d}{d x} (- \frac{8 x}{( x ^{2} - 4 ) ^{2}})

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