derivative f(x)=(3x+2)(4x^2+3)

Lösung

ableitung von

f (x) = (3 x + 2) (4 x^{2} + 3)

36 x^{2} + 16 x + 9

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = 3 x + 2, g = 4 x^{2} + 3

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

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

\frac{d}{d x} (4 x^{2} + 3) = 8 x

= 3 (4 x^{2} + 3) + 8 x (3 x + 2)

Vereinfache

3 (4 x^{2} + 3) + 8 x (3 x + 2) : 36 x^{2} + 16 x + 9

= 36 x^{2} + 16 x + 9

\frac{\partial}{\partial x} (ln (x^{3} + y^{2}))

\frac{d}{d x} (sec (\frac{x}{2}))

\int e^{x + y + z} d x

\int_{0}^{1} (7 e^{x} - 7 x e^{x^{2}}) d x

d er i v a t i v e f (x) = 3 x ln (19 x)