(\partial)/(\partial x)(xe^{sqrt(19xy)})

Lösung

\frac{\partial}{\partial x} (x e^{19 x y})

\frac{19 e ^{19 x y} x y}{2} + e^{19 x y}

Schritte zur Lösung

\frac{\partial}{\partial x} (x e^{19 x y})

Vereinfache

x e^{19 x y} : e^{19 x y} x

= \frac{\partial}{\partial x} (e^{19 x y} x)

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = e^{19 x y}, g = x

= \frac{\partial}{\partial x} (e^{19 x y}) x + \frac{\partial}{\partial x} (x) e^{19 x y}

\frac{\partial}{\partial x} (e^{19 x y}) = \frac{19 y e ^{19 y x}}{2 x}

\frac{\partial}{\partial x} (x) = 1

= \frac{19 y e ^{19 y x}}{2 x} x + 1 \cdot e^{19 x y}

Vereinfache

\frac{19 y e ^{19 y x}}{2 x} x + 1 \cdot e^{19 x y} : \frac{19 e ^{19 x y} x y}{2} + e^{19 x y}

= \frac{19 e ^{19 x y} x y}{2} + e^{19 x y}

\int_{0}^{2} (2 x^{2} - 3 x + 2) d x

x \to c lim (x^{2} + x + 1)

y^{^{''}} + y^{^{'}} + (π^{2} + \frac{1}{4}) y = 0

t an g e n t 7 - x^{2}

d er i v a t i v e (ln (x))^{6}