derivative of 2ax^3-(x^2/b+c)

Lösung

\frac{d}{d x} (2 a x^{3} - \frac{x ^{2}}{b} + c)

6 a x^{2} - \frac{2 x}{b}

Schritte zur Lösung

\frac{d}{d x} (2 a x^{3} - \frac{x ^{2}}{b} + c)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (2 a x^{3}) - \frac{d}{d x} (\frac{x ^{2}}{b}) + \frac{d c}{d x}

\frac{d}{d x} (2 a x^{3}) = 6 a x^{2}

\frac{d}{d x} (\frac{x ^{2}}{b}) = \frac{2 x}{b}

\frac{d c}{d x} = 0

= 6 a x^{2} - \frac{2 x}{b} + 0

Vereinfache

= 6 a x^{2} - \frac{2 x}{b}

\frac{\partial}{\partial x} (2 x^{6} y^{5} + 3 x^{5} y^{6})

\int 7 x^{7} e^{- x^{4}} d x

(ln (5 x))^{^{'}}

\int_{0}^{2} \frac{x}{1 + 2 x ^{2}} d x

\frac{d}{d x} (\frac{e ^{x}}{4 x ^{2}})