(\partial)/(\partial x)(x^3-3x+3xy^2)

Lösung

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

3 x^{2} - 3 + 3 y^{2}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

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

= 3 x^{2} - 3 + 3 y^{2}

d er i v a t i v e x^{2} 25 - x^{2}

l a pl a ce t r an s f or m sin (2 t + \frac{π}{4})

y^{^{''}} + 8 y^{^{'}} + 32 y = 0, y (0) = 0, y^{^{'}} (0) = 0

\int \frac{- x}{1 - x ^{2}} d x

\frac{d}{d x} (c x e^{- 2 x})