d/(d{y)}({x}^{{y}^{{z}}})

Lösung

\frac{d}{d y} (x^{y^{z}})

ln (x) z x^{y^{z}} y^{z - 1}

Schritte zur Lösung

\frac{d}{d y} (x^{y^{z}})

Wende Exponentenregel an:

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

x^{y^{z}} = e^{y^{z} l n (x)}

= \frac{d}{d y} (e^{y^{z} l n (x)})

Wende die Kettenregel an:

e^{y^{z} l n (x)} \frac{d}{d y} (y^{z} ln (x))

= e^{y^{z} l n (x)} \frac{d}{d y} (y^{z} ln (x))

\frac{d}{d y} (y^{z} ln (x)) = ln (x) z y^{z - 1}

= e^{y^{z} l n (x)} ln (x) z y^{z - 1}

e^{y^{z} l n (x)} = x^{y^{z}}

= ln (x) z x^{y^{z}} y^{z - 1}

d er i v a t i v e f (x) = \frac{5}{1 - 9 x}

d er i v a t i v e f (x) = 6 e^{x} + 4 x^{2}

\frac{\partial}{\partial y} (cos (12 x) sin (3 y))

\int \frac{1}{9 - y ^{2}} d y

in v erse l a pl a ce \frac{1}{( z ^{2} + 1 ) ^{2}}