# Derivative of $\operatorname{acos}{\left(x \right)}$

The calculator will find the derivative of $\operatorname{acos}{\left(x \right)}$, with steps shown.

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Find $\frac{d}{dx} \left(\operatorname{acos}{\left(x \right)}\right)$.

### Solution

The derivative of the inverse cosine is $\frac{d}{dx} \left(\operatorname{acos}{\left(x \right)}\right) = - \frac{1}{\sqrt{1 - x^{2}}}$:

$${\color{red}\left(\frac{d}{dx} \left(\operatorname{acos}{\left(x \right)}\right)\right)} = {\color{red}\left(- \frac{1}{\sqrt{1 - x^{2}}}\right)}$$

Thus, $\frac{d}{dx} \left(\operatorname{acos}{\left(x \right)}\right) = - \frac{1}{\sqrt{1 - x^{2}}}$.

$\frac{d}{dx} \left(\operatorname{acos}{\left(x \right)}\right) = - \frac{1}{\sqrt{1 - x^{2}}}$A