(\partial)/(\partial y)(x^{y^2})

Lösung

\frac{\partial}{\partial y} (x^{y^{2}})

2 y x^{y^{2}} ln (x)

Schritte zur Lösung

\frac{\partial}{\partial y} (x^{y^{2}})

Behandle

x

als Konstante

Wende Exponentenregel an:

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

x^{y^{2}} = e^{y^{2} l n (x)}

= \frac{\partial}{\partial y} (e^{y^{2} l n (x)})

Wende die Kettenregel an:

e^{y^{2} l n (x)} \frac{\partial}{\partial y} (y^{2} ln (x))

= e^{y^{2} l n (x)} \frac{\partial}{\partial y} (y^{2} ln (x))

\frac{\partial}{\partial y} (y^{2} ln (x)) = 2 y ln (x)

= e^{y^{2} l n (x)} \cdot 2 y ln (x)

e^{y^{2} l n (x)} = x^{y^{2}}

= 2 y x^{y^{2}} ln (x)

\int \frac{1}{x ^{3}} 1 - \frac{1}{x ^{2}} d x

\frac{d}{d x} (3 x (x + 3))

\int_{1}^{2} \frac{1}{x} - x d x

\int cot (y) d y

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