Derivative of Inverse

f(f−1(x))=x(f(f−1(x)))′=x′f′(f−1(x))(f−1(x))′=1(f−1(x))′=1f′(f−1(x))\begin{aligned} f\left(f^{-1}(x)\right)&=x\\ \left(f\left(f^{-1}(x)\right)\right)^\prime&=x^\prime\\ f^\prime\left(f^{-1}(x)\right)\left(f^{-1}(x)\right)^\prime&=1\\ \left(f^{-1}(x)\right)^\prime&=\boxed{\frac{1}{f^\prime\left(f^{-1}(x)\right)}} \end{aligned}

#Calculus

Note by Gandoff Tan
1 year, 6 months ago

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Nice

Rudra Pratap - 10 months, 1 week ago
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