(\partial)/(\partial y)(xe^{5xy})

Lösung

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

5 e^{5 x y} x^{2}

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Kettenregel an:

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

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

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

= x e^{5 x y} \cdot 5 x

Vereinfache

x e^{5 x y} \cdot 5 x : 5 e^{5 x y} x^{2}

= 5 e^{5 x y} x^{2}

\frac{\partial}{\partial x} (2 x^{2} + 4 y^{2} + \frac{1}{2})

\int (\frac{1}{x ^{4}} - x^{4} - \frac{1}{4}) d x

\int cos (2 x) \cdot sin (2 x) d x

\int \frac{1 - sin ( x )}{cos ^{2} ( x )} d x

n = 0 \sum \infty \frac{1}{n ( n + 1 )}