Chapter 05 · Derivatives
05.10
Derivatives of Inverse Functions
The slope of an inverse function is the reciprocal of the original slope. From that, the derivatives of arcsin, arccos and arctan.
About 40 minutes
You'll learn to
- →Explain why the slopes of f and f⁻¹ at mirror-image points are reciprocals
- →Use (f⁻¹)'(b) = 1/f'(a), where f(a) = b, without finding f⁻¹
- →Derive and use the derivatives of arcsin, arccos and arctan
- →Combine inverse trig derivatives with the chain rule