Category:Derivative of Inverse Function
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This category contains pages concerning Derivative of Inverse Function:
Let $I = \closedint a b$ and $J = \closedint c d$ be closed real intervals.
Let $I^o = \openint a b$ and $J^o = \openint c d$ be the corresponding open real intervals.
Let $f: I \to J$ be a real function which is continuous on $I$ and differentiable on $I^o$ such that $J = f \sqbrk I$.
Let either:
- $\forall x \in I^o: D \map f x > 0$
or:
- $\forall x \in I^o: D \map f x < 0$
Then:
- $f^{-1}: J \to I$ exists and is continuous on $J$
- $f^{-1}$ is differentiable on $J^o$
- $\forall y \in J^o: D \map {f^{-1} } y = \dfrac 1 {D \map f x}$
Pages in category "Derivative of Inverse Function"
The following 4 pages are in this category, out of 4 total.