The Derivative of the Inverse Trigonometric Functions

Now that we know how to compute the derivative of a inverse function, we can apply this technique to learn some new derivatives.

For example, we can now compute the derivatives of the inverse trigonometric functions. By using this technique, we will find that:

\begin{aligned} \frac{d}{dx}\left(\arcsin{x}\right) &= \frac1{\sqrt{1-x^2}} \\ \frac{d}{dx}\left(\arccos{x}\right) &= -\frac1{\sqrt{1-x^2}} \\ \frac{d}{dx}\left(\arctan{x}\right) &= \frac1{1+x^2} \\ \end{aligned}

With these results, we are now able to calculate derivatives for functions that include the inverse trigonmetric functions.

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