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

Lösung

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

\frac{e ^{2 x y} x ^{\frac{3}{2}} y}{2} + 2 e^{2 x y} x

Schritte zur Lösung

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

Vereinfache

x^{2} e^{2 x y} : e^{2 x y} x^{2}

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

Behandle

y

als Konstante

Wende die Produktregel an:

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

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

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

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

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

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

\frac{y e ^{2 y x}}{2 x} x^{2} = \frac{e ^{2 x y} x ^{\frac{3}{2}} y}{2}

= \frac{e ^{2 x y} x ^{\frac{3}{2}} y}{2} + 2 e^{2 x y} x

y^{^{'}} - 3 y = e^{2 t}

ma c l a u r in 1 - (1 - x)^{2 - 1}

t a y l or ln (1 - 4 x)

\int e^{t^{2} - t} d t

\frac{\partial}{\partial x} (ln (5 x + 3 y))