(\partial)/(\partial y)(x^{5y})

Lösung

\frac{\partial}{\partial y} (x^{5 y})

5 x^{5 y} ln (x)

Schritte zur Lösung

\frac{\partial}{\partial y} (x^{5 y})

Behandle

x

als Konstante

Wende Exponentenregel an:

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

x^{5 y} = e^{5 y l n (x)}

= \frac{\partial}{\partial y} (e^{5 y l n (x)})

Wende die Kettenregel an:

e^{5 y l n (x)} \frac{\partial}{\partial y} (5 y ln (x))

= e^{5 y l n (x)} \frac{\partial}{\partial y} (5 y ln (x))

\frac{\partial}{\partial y} (5 y ln (x)) = 5 ln (x)

= e^{5 y l n (x)} \cdot 5 ln (x)

e^{5 y l n (x)} = x^{5 y}

= 5 x^{5 y} ln (x)

\int (x^{5}) d x

\int sin (x + \frac{π}{4}) d x

\int \frac{1}{e ^{π}} d x

\int_{0}^{\frac{π}{3}} x sin (2 x) d x

in v erse l a pl a ce \frac{1}{( s + 1 ) ^{3}}