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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

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

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

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

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

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

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

\int \frac{2 x ^{2}}{9 - x ^{2}} d x

\int_{0}^{1} 2 π (2 - y) (7 - 7 y^{2}) d y

in v erse l a pl a ce \frac{3}{4 s}

\frac{d}{d x} (sec^{2} (x^{3}))

x \to 2 lim (- x + 7)