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

The derivative of (f^{-1})(d) is -d/(f^2)

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

The first derivative of (f^{-1})(d) is -d/(f^2)

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derivative of

(f^{- 1}) (d)

- \frac{d}{f ^{2}}

Solution steps

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

Treat

d

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= d \frac{d}{df} (f^{- 1})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= d (- 1 \cdot f^{- 1 - 1})

Simplify

d (- 1 \cdot f^{- 1 - 1}) : - \frac{d}{f ^{2}}

= - \frac{d}{f ^{2}}

What is the derivative of (f^{-1})(d) ?
The derivative of (f^{-1})(d) is -d/(f^2)
What is the first derivative of (f^{-1})(d) ?
The first derivative of (f^{-1})(d) is -d/(f^2)