derivative of a^{{f}(x})

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

a^{f (x)} = e^{f (x) l n (a)}

= \frac{d}{d x} (e^{f (x) l n (a)})

Wende die Kettenregel an:

e^{f (x) l n (a)} \frac{d}{d x} (f (x) ln (a))

= e^{f (x) l n (a)} \frac{d}{d x} (f (x) ln (a))

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

= e^{f (x) l n (a)} ln (a) \frac{d}{d x} (f (x))

e^{f (x) l n (a)} = a^{f (x)}

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

\int e^{- θ} cos (2 θ) d θ

\int \frac{19 arctan ( x )}{x ^{2}} d x

x \to 0 lim (\frac{( x + 1 ) ^{3} - 1}{x})

s l o p e \frac{1}{x - 3}

\frac{\partial}{\partial x} (\frac{s - 2 r}{t})