Derivative of arccos x

\frac{d}{dx}\left[\arccos\left(x\right)\right] = -\frac{1}{\sqrt{-x^{2} + 1}}.

Differentiate again: \frac{d^2}{dx^2}\left[\arccos\left(x\right)\right] = -\frac{x}{\left(-x^{2} + 1\right)^{\frac{3}{2}}}.

Plug into the derivative: f'(0.2) = -1.02062. That is the slope of the tangent line there; drag the graph to see it.

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

\frac{d}{dx}\left[\arccos\left(x\right)\right] = -\frac{1}{\sqrt{-x^{2} + 1}}

Since arccos x = π/2 − arcsin x, its derivative is just the negative of arcsin’s: −1/√(1 − x²). Only defined for −1 < x < 1.

Inverse trig rule
$\frac{d}{dx}\left[\arccos\left(x\right)\right] = -\frac{1}{\sqrt{-x^{2} + 1}}$

Drag the graph · at x = 0.29 the slope is -1.0449, the height of the dashed curve.

Questions students ask

What is the derivative of arccos x?

$\frac{d}{dx}\left[\arccos\left(x\right)\right] = -\frac{1}{\sqrt{-x^{2} + 1}}$ .

What is the second derivative of arccos x?

Differentiate again: $\frac{d^2}{dx^2}\left[\arccos\left(x\right)\right] = -\frac{x}{\left(-x^{2} + 1\right)^{\frac{3}{2}}}$ .

What is the slope of arccos x at x = 0.2?

Plug into the derivative: $f'(0.2) = -1.02062$ . That is the slope of the tangent line there; drag the graph to see it.

How do you find the derivative of arccos x?

Since arccos x = π/2 − arcsin x, its derivative is just the negative of arcsin’s: −1/√(1 − x²). Only defined for −1 < x < 1.

What is the integral of arccos x?

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