(\partial)/(\partial y)(y^2e^{xy-3})

Lösung

\frac{\partial}{\partial y} (y^{2} e^{x y - 3})

2 y e^{x y - 3} + e^{x y - 3} x y^{2}

Schritte zur Lösung

\frac{\partial}{\partial y} (y^{2} e^{x y - 3})

Behandle

x

als Konstante

Wende die Produktregel an:

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

f = y^{2}, g = e^{x y - 3}

= \frac{\partial}{\partial y} (y^{2}) e^{x y - 3} + \frac{\partial}{\partial y} (e^{x y - 3}) y^{2}

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

\frac{\partial}{\partial y} (e^{x y - 3}) = e^{x y - 3} x

= 2 y e^{x y - 3} + e^{x y - 3} x y^{2}

x \to - 5 lim (\frac{3}{x + 5})

\int \frac{1}{- 2 y} d y

d er i v a t i v e y = 3 sin (\frac{x π}{90})

\int 3 x e^{5 x^{2}} d x

\frac{d y}{d x} = \frac{2 x + sec ^{2} ( x )}{4 y}, y (π) = 1