(\partial)/(\partial x)(2xye^{xy^2})

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

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

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

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

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

= 2 y (1 \cdot e^{x y^{2}} + e^{x y^{2}} y^{2} x)

Vereinfache

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

t an g e n t f (x) = tan (x), (\frac{π}{4}, 1)

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

y (1 + x^{2}) y^{^{'}} - x (8 + y^{2}) = 0

ma c l a u r in a^{x}

\frac{\partial}{\partial x} (ln (x^{2} + x))