derivative (3x^2+7)(6x+3)

Lösung

ableitung von

(3 x^{2} + 7) (6 x + 3)

54 x^{2} + 18 x + 42

Schritte zur Lösung

\frac{d}{d x} ((3 x^{2} + 7) (6 x + 3))

Wende die Produktregel an:

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

f = 3 x^{2} + 7, g = 6 x + 3

= \frac{d}{d x} (3 x^{2} + 7) (6 x + 3) + \frac{d}{d x} (6 x + 3) (3 x^{2} + 7)

\frac{d}{d x} (3 x^{2} + 7) = 6 x

\frac{d}{d x} (6 x + 3) = 6

= 6 x (6 x + 3) + 6 (3 x^{2} + 7)

Vereinfache

6 x (6 x + 3) + 6 (3 x^{2} + 7) : 54 x^{2} + 18 x + 42

= 54 x^{2} + 18 x + 42

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

d er i v a t i v e \frac{( ( x ^{6} ) - 1 )}{( ( x ^{6} ) + 1 )}

d er i v a t i v e y = 3 cos (x) + 7 e x + ln (x^{2} + 1)

d er i v a t i v e f (x) = \frac{4 x - 1}{x}

d er i v a t i v e 2^{z}