(\partial)/(\partial y)(5y^2e^{5xy})

Lösung

\frac{\partial}{\partial y} (5 y^{2} e^{5 x y})

5 (2 y e^{5 x y} + e^{5 x y} \cdot 5 x y^{2})

Schritte zur Lösung

\frac{\partial}{\partial y} (5 y^{2} e^{5 x y})

Behandle

x

als Konstante

Entferne die Konstante:

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

= 5 \frac{\partial}{\partial y} (y^{2} e^{5 x y})

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y^{2}, g = e^{5 x y}

= 5 (\frac{\partial}{\partial y} (y^{2}) e^{5 x y} + \frac{\partial}{\partial y} (e^{5 x y}) y^{2})

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

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

= 5 (2 y e^{5 x y} + e^{5 x y} \cdot 5 x y^{2})

\int sin (wt) d t

x y^{^{'}} = \frac{1}{y ^{3}}

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

x \to \infty lim (\frac{x}{0})

\int \frac{5 x 3 5 x ^{2} + 1}{3} d x