(\partial)/(\partial x)(z^{x^y})

Lösung

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

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

Schritte zur Lösung

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

Behandle

z, y

als Konstanten

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

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

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

t an g e n t f (x) = \frac{x}{x ^{2} + 81}

a re a x = 2 y^{2} - 5, x = y^{2} + 4

d er i v a t i v e y = 2 x - 5

\int x^{- 12} d x

d er i v a t i v e f (x) = 6 x^{3} - 9 x + 4