Derivative of `acos(x)`

Step-by-step differentiation

Answer

\frac{d}{d x} [cos^{- 1} (x)]

- \frac{1}{1 - x ^{2}}

Step-by-step solution

1Derivative of arccos
$\frac{d}{d x} [cos^{- 1} (x)] = \frac{- 1}{1 - ( x ) ^{2}}$
The derivative of $arccos (x)$ is $\frac{- 1}{1 - x ^{2}}$ .
✓Final Answer
$\frac{d}{d x} [cos^{- 1} (x)] = - \frac{1}{1 - x ^{2}}$
The first derivative simplifies to $- \frac{1}{1 - x ^{2}}$ .

Understanding this derivative

Differentiating acos(x) is a single-rule problem: everything follows from the inverse trig derivatives. That makes it a good expression for isolating and practicing that one technique.

Inverse trigonometric functions have algebraic derivatives — expressions involving square roots and rational functions rather than other trig functions — which is why the result looks structurally different from the input.

A good way to verify a derivative by hand is to compare it against the step-by-step breakdown above — each step names the rule being applied, so you can pinpoint exactly where your own work diverges if the answers differ.

Learn the rules used here

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Derivative of acos(x)

Step-by-step solution

Understanding this derivative

Learn the rules used here

Derivative of `acos(x)`