Derivative of acos(x)

Step-by-step solution

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

   The derivative of $\arccos (x)$ is $\frac{-1}{\sqrt{1-x^2}}$.

2. ✓Final Answer
   $$\frac{d}{dx}\left[{\cos }^{-1}\left(x\right)\right]=-\frac{1}{\sqrt{1-x^2}}$$

   The first derivative simplifies to $-\frac{1}{\sqrt{1-x^2}}$.