What is the derivative of cot(x^{-2}) ?

The derivative of cot(x^{-2}) is (2csc^2(1/(x^2)))/(x^3)

What is the first derivative of cot(x^{-2}) ?

The first derivative of cot(x^{-2}) is (2csc^2(1/(x^2)))/(x^3)

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derivative of

cot (x^{- 2})

\frac{2 csc ^{2} ( \frac{1}{x ^{2}} )}{x ^{3}}

Solution steps

\frac{d}{d x} (cot (x^{- 2}))

Apply the chain rule:

- csc^{2} (x^{- 2}) \frac{d}{d x} (x^{- 2})

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

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

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

Simplify

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

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

3 x^{2} y^{2}

\frac{e ^{2} x}{2}

lo g_{10} ((3 x + 2)^{3})

cos^{2} (\frac{x}{2})

\frac{d}{d t} (\frac{1}{2 \cdot a \cdot t ^{2}})

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