derivative of x^4+4x^3-2x^2-12x

Lösung

\frac{d}{d x} (x^{4} + 4 x^{3} - 2 x^{2} - 12 x)

4 x^{3} + 12 x^{2} - 4 x - 12

Schritte zur Lösung

\frac{d}{d x} (x^{4} + 4 x^{3} - 2 x^{2} - 12 x)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (x^{4}) + \frac{d}{d x} (4 x^{3}) - \frac{d}{d x} (2 x^{2}) - \frac{d}{d x} (12 x)

\frac{d}{d x} (x^{4}) = 4 x^{3}

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

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

\frac{d}{d x} (12 x) = 12

= 4 x^{3} + 12 x^{2} - 4 x - 12

\frac{d}{d x} (1 0^{- 2 x})

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

in v erse l a pl a ce \frac{8}{( 9 s ^{2} + 12 s + 4 ) ( s )}

\int x \cdot e^{x^{2}} d x

\frac{d ^{2} x}{d t ^{2}} + 9 x = - sin (3 t)