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

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

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

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

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

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

Solution steps

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

Simplify

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

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

Take the constant out:

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

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

\frac{d}{d t} (t^{2} - 1)

\int \frac{sin ( x )}{2 e ^{x}} d x

\int_{- 3}^{3} ∣ x ∣ - (x^{2} - 6) d x

- \frac{1}{2} \cdot \frac{1}{( x ^{2} + 1 ) ^{2}}

\int_{0}^{2} (2 x - x^{2})^{2} d x

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