Derivative of cot x

Differentiate again: \frac{d^2}{dx^2}\left[\cot\left(x\right)\right] = 2 \csc^{2}\left(x\right) \cot\left(x\right).

Plug into the derivative: f'(1.8) = -1.05443. That is the slope of the tangent line there; drag the graph to see it.

\frac{d}{dx}\left[\cot\left(x\right)\right] = -\csc^{2}\left(x\right)

cot x = cos x / sin x; the quotient rule gives −(sin²x + cos²x)/sin²x = −csc²x.

Trig rule
$\frac{d}{dx}\left[\cot\left(x\right)\right] = -\csc^{2}\left(x\right)$

Drag the graph · at x = 1.96 the slope is -1.1682, the height of the dashed curve.

Questions students ask

What is the derivative of cot x?

$\frac{d}{dx}\left[\cot\left(x\right)\right] = -\csc^{2}\left(x\right)$ .

What is the second derivative of cot x?

Differentiate again: $\frac{d^2}{dx^2}\left[\cot\left(x\right)\right] = 2 \csc^{2}\left(x\right) \cot\left(x\right)$ .

What is the slope of cot x at x = 1.8?

Plug into the derivative: $f'(1.8) = -1.05443$ . That is the slope of the tangent line there; drag the graph to see it.

How do you find the derivative of cot x?

cot x = cos x / sin x; the quotient rule gives −(sin²x + cos²x)/sin²x = −csc²x.

What is the integral of cot x?

Use the integral calculator to find the antiderivative of cot x step by step.