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

Lösung

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

y e^{x^{2} - x y} (2 x - y)

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

= y e^{x^{2} - x y} (2 x - y)

\int 6 sin (6 x) d x

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

\int \frac{x ^{2}}{x ^{6} + 4} d x

d er i v a t i v e f (x) = - 5 csc (x) + sec (x)

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