derivative of (3x^2-3x+1x^3)

Lösung

\frac{d}{d x} ((3 x^{2} - 3 x + 1) x^{3})

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

Schritte zur Lösung

\frac{d}{d x} ((3 x^{2} - 3 x + 1) x^{3})

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 3 x^{2} - 3 x + 1, g = x^{3}

= \frac{d}{d x} (3 x^{2} - 3 x + 1) x^{3} + \frac{d}{d x} (x^{3}) (3 x^{2} - 3 x + 1)

\frac{d}{d x} (3 x^{2} - 3 x + 1) = 6 x - 3

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

= (6 x - 3) x^{3} + 3 x^{2} (3 x^{2} - 3 x + 1)

Vereinfache

(6 x - 3) x^{3} + 3 x^{2} (3 x^{2} - 3 x + 1) : 15 x^{4} - 12 x^{3} + 3 x^{2}

= 15 x^{4} - 12 x^{3} + 3 x^{2}

\int_{0}^{3} (3 - x) x d x

\frac{d}{d y} (x (y) z (y))

t a y l or x e^{x^{2}}, 0

\int \frac{21}{4 + 25 r ^{2}} d r

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