MathLiveDerivative of an inverse function
Gives the derivative of an inverse function as the reciprocal of the derivative of the original function, evaluated at the corresponding point. It is used when f is differentiable and invertible and its inverse's derivative is hard to find directly.
\frac{\mathrm{d}}{\mathrm{d}y}f^{-1}(y) = \frac{1}{\frac{\mathrm{d}}{\mathrm{d}x}f\left(f^{-1}(y)\right)}What the symbols mean
| an invertible, differentiable function | |
| the inverse function of f | |
| the input of f, with x = f^{-1}(y) | |
| the input of the inverse function f^{-1} |
About this formula
- FieldMathematics
- TopicDifferential calculus
- LevelUniversity
- Also calledinverse function differentiation, inverse function rule, derivative of inverse function, differentiating inverse functions, inverse function theorem derivative, d/dy f inverse
- SourceWikidata Q2143416
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