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

Lösung

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

12 x^{3} + 6 x^{2} + 2 x

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

\frac{d}{d x} (2) = 0

= 12 x^{3} + 6 x^{2} + 2 x - 0

Vereinfache

= 12 x^{3} + 6 x^{2} + 2 x

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

\frac{d y}{d x} = - \frac{y ( x + y + 1 )}{x + 2 y}

\int \frac{1}{e ^{x} + 3} d x

d er i v a t i v e y = sin (x) ln (2 x)

\frac{d}{d x} (\frac{6 arctan ( 2 x )}{5 e ^{3 x}})