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

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

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

\int_{2}^{\infty} 2 e^{- 2 x} d x

\int 2 b x^{3} d x

\frac{d}{d x} ((5 x^{2} - 7) (3 x^{2} - 2 x + 1))

t an g e n t y = \frac{x}{4 - x}, (3, 3)

- \frac{1}{4 x ^{\frac{3}{2}}}