Derivative of f^(-1) (Inverse Functions)
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- Let y=f(x)y=f(x)y=f(x), so that dydx=f′(x)\frac{\text dy}{\text dx}=f'(x)dxdy=f′(x) Then dxdy=1f′(x)\frac{\text dx}{\text dy}=\frac1{f'(x)}dydx=f′(x)1 Now, substitute x=f−1(x…
By Tim Ratigan
- Let y=f−1(x)y=f^{-1}(x)y=f−1(x). Then, f(y)=xf(y)=xf(y)=x. Differentiating implicitly, ddx(f(y))=1\frac d{dx}(f(y)) = 1dxd(f(y))=1 f′(y)dydx=1f'(y)\frac{dy}{dx} = 1f′(y)dxdy=1…
By Alexander Duan
- Derivative of an Inverse Function We know how to take lots of derivatives by now. But we're still missing some fundamental derivatives of inverse functions, like arcsinx\arcsin…
By Rajiv Movva, Victor Wang, Victor Wang, DifferentialMaker