(\partial)/(\partial x)(4x^3+2xy^2+1)

Lösung

\frac{\partial}{\partial x} (4 x^{3} + 2 x y^{2} + 1)

12 x^{2} + 2 y^{2}

Schritte zur Lösung

\frac{\partial}{\partial x} (4 x^{3} + 2 x y^{2} + 1)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (4 x^{3}) + \frac{\partial}{\partial x} (2 x y^{2}) + \frac{\partial}{\partial x} (1)

\frac{\partial}{\partial x} (4 x^{3}) = 12 x^{2}

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

\frac{\partial}{\partial x} (1) = 0

= 12 x^{2} + 2 y^{2} + 0

Vereinfache

= 12 x^{2} + 2 y^{2}

\int x^{2} arctan (4 x) d x

\frac{d}{d x} (- 15)

\frac{\partial}{\partial y} (sin (4 y) e^{- 5 x})

\frac{d}{d x} (\frac{x ^{7} - 4 x ^{3} + 12 x}{x ^{3}})

x \to 0 lim (\frac{1}{e ^{x} - 1})