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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial x} (3 x y) = 3 y

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

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

\int \frac{x}{2 e ^{x}} d x

d er i v a t i v e 6 x^{4} (7 - 6 x)^{3}

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

d er i v a t i v e f (x) = 500 - y - \frac{4 y}{y + 3}

\int \frac{1}{4 x ^{2} + 5} d x