Find the Derivative – d/dx cot(1/x)

$\cot (\frac{1}{x})$

Differentiate using the chain rule, which states that $\frac{d}{d x} [f (g (x))]$ is $f' (g (x)) g' (x)$ where $f (x) = \cot (x)$ and $g (x) = \frac{1}{x}$ .

Tap for more steps…

To apply the Chain Rule, set $u$ as $\frac{1}{x}$ .

$\frac{d}{d u} [\cot (u)] \frac{d}{d x} [\frac{1}{x}]$

The derivative of $\cot (u)$ with respect to $u$ is $- \csc^{2} (u)$ .

$- \csc^{2} (u) \frac{d}{d x} [\frac{1}{x}]$

Replace all occurrences of $u$ with $\frac{1}{x}$ .

$- \csc^{2} (\frac{1}{x}) \frac{d}{d x} [\frac{1}{x}]$

Differentiate using the Power Rule.

Tap for more steps…

Rewrite $\frac{1}{x}$ as $x^{- 1}$ .

$- \csc^{2} (\frac{1}{x}) \frac{d}{d x} [x^{- 1}]$

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = - 1$ .

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

Multiply.

Tap for more steps…

Multiply $- 1$ by $- 1$ .

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

Multiply $\csc^{2} (\frac{1}{x})$ by $1$ .

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

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Combine $\csc^{2} (\frac{1}{x})$ and $\frac{1}{x^{2}}$ .

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

Find the Derivative – d/dx cot(1/x)

Download our
App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Download our App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Download our
App from the store