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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

e^{x^{y} l n (y)} ln (y) y x^{y - 1} : y^{x^{y} + 1} x^{y - 1} ln (y)

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

y^{^{''}} - 4 y^{^{'}} + 4 y = t^{- 4} e^{2 t}

l a pl a ce t r an s f or m t^{2} \cdot e^{- 3 t}

\frac{d}{d x} (\frac{x}{10} - \frac{10}{x})

\int 20 θ sec^{2} (θ) d θ

\int \frac{\frac{d}{1} ( x )}{x} d x