What is the derivative of f(x^{-1}(x)) ?

The derivative of f(x^{-1}(x)) is derivative of {f}(x)

What is the first derivative of f(x^{-1}(x)) ?

The first derivative of f(x^{-1}(x)) is derivative of {f}(x)

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\frac{d}{d x} (f (x) (x)^{- 1} (x))

\frac{d}{d x} (f (x))

Solution steps

\frac{d}{d x} (f (x) (x)^{- 1} (x))

Simplify

f (x) (x)^{- 1} (x) : f (x)

= \frac{d}{d x} (f (x))

= \frac{d}{d x} (f (x))

What is the derivative of f(x^{-1}(x)) ?
The derivative of f(x^{-1}(x)) is derivative of {f}(x)
What is the first derivative of f(x^{-1}(x)) ?
The first derivative of f(x^{-1}(x)) is derivative of {f}(x)