(\partial)/(\partial x)(5x^2y+2xy^3+3y^2)

Lösung

\frac{\partial}{\partial x} (5 x^{2} y + 2 x y^{3} + 3 y^{2})

2 y^{3} + 10 x y

Schritte zur Lösung

\frac{\partial}{\partial x} (5 x^{2} y + 2 x y^{3} + 3 y^{2})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (5 x^{2} y) + \frac{\partial}{\partial x} (2 x y^{3}) + \frac{\partial}{\partial x} (3 y^{2})

\frac{\partial}{\partial x} (5 x^{2} y) = 10 y x

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

\frac{\partial}{\partial x} (3 y^{2}) = 0

= 10 y x + 2 y^{3} + 0

Vereinfache

= 2 y^{3} + 10 x y

x^{^{''}} + x = 0, x (0) = 0, x^{^{'}} (0) = 0

\int_{- 4}^{4} (16 - x^{2}) d x

d er i v a t i v e f (x) = x^{- 2}

\frac{d}{d x} (lo g_{10} (e^{x}))

\frac{d y}{d t} = - \frac{1}{2} y