(\partial)/(\partial y)(x^{6y})

Lösung

\frac{\partial}{\partial y} (x^{6 y})

6 x^{6 y} ln (x)

Schritte zur Lösung

\frac{\partial}{\partial y} (x^{6 y})

Behandle

x

als Konstante

Wende Exponentenregel an:

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

x^{6 y} = e^{6 y l n (x)}

= \frac{\partial}{\partial y} (e^{6 y l n (x)})

Wende die Kettenregel an:

e^{6 y l n (x)} \frac{\partial}{\partial y} (6 y ln (x))

= e^{6 y l n (x)} \frac{\partial}{\partial y} (6 y ln (x))

\frac{\partial}{\partial y} (6 y ln (x)) = 6 ln (x)

= e^{6 y l n (x)} \cdot 6 ln (x)

e^{6 y l n (x)} = x^{6 y}

= 6 x^{6 y} ln (x)

\int_{- 1}^{1} (x^{2} - x - 1) d x

\int t^{3} e^{- s t} d t

x \to - 6 lim (∣ x + 6 ∣)

e x p an d 3 7 x^{2} + 7 x + 5 \cdot (5 x - 3)

\int \frac{1}{3 cos ( 5 x - \frac{π}{4} )} d x