derivative of-3/2 x^3+2/5 x^2-4

Lösung

\frac{d}{d x} (- \frac{3}{2} x^{3} + \frac{2}{5} x^{2} - 4)

- \frac{9 x ^{2}}{2} + \frac{4 x}{5}

Schritte zur Lösung

\frac{d}{d x} (- \frac{3}{2} x^{3} + \frac{2}{5} x^{2} - 4)

Vereinfache

- \frac{3}{2} x^{3} + \frac{2}{5} x^{2} - 4 : - \frac{3 x ^{3}}{2} + \frac{2 x ^{2}}{5} - 4

= \frac{d}{d x} (- \frac{3 x ^{3}}{2} + \frac{2 x ^{2}}{5} - 4)

Wende die Summen-/Differenzregel an:

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

= - \frac{d}{d x} (\frac{3 x ^{3}}{2}) + \frac{d}{d x} (\frac{2 x ^{2}}{5}) - \frac{d}{d x} (4)

\frac{d}{d x} (\frac{3 x ^{3}}{2}) = \frac{9 x ^{2}}{2}

\frac{d}{d x} (\frac{2 x ^{2}}{5}) = \frac{4 x}{5}

\frac{d}{d x} (4) = 0

= - \frac{9 x ^{2}}{2} + \frac{4 x}{5} - 0

Vereinfache

= - \frac{9 x ^{2}}{2} + \frac{4 x}{5}

\int 50 x^{3} 1 - 25 x^{2} d x

x \to - 2 lim (\frac{- 3}{2 - x})

\frac{\partial}{\partial x} (lo g_{5} (x))

d er i v a t i v e ln (\frac{2 x + 1}{x ^{2} - 3})

d er i v a t i v e g (x) = 5 - x