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

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

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

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

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derivative of

f (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 tan^{3} (5 x) d x

y = (ln ∣ x + 8 ∣)^{7}

y^{^{'}} = \frac{( 3 y ^{2} - 9 )}{2 x y}

\int (sin (x))^{3} (cos (x))^{3} d x

e^{a r c s i n (x)}

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