derivative of (3x^3-4(-4x-3))

Lösung

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

- 48 x^{3} - 27 x^{2} + 16

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = 3 x^{3} - 4, g = - 4 x - 3

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

\frac{d}{d x} (3 x^{3} - 4) = 9 x^{2}

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

= 9 x^{2} (- 4 x - 3) + (- 4) (3 x^{3} - 4)

Vereinfache

9 x^{2} (- 4 x - 3) + (- 4) (3 x^{3} - 4) : - 48 x^{3} - 27 x^{2} + 16

= - 48 x^{3} - 27 x^{2} + 16

4 x^{2} y^{^{'}} = y^{^{'}} + 9 x e^{- y}

\int 1 x d x

d er i v a t i v e y = 19 sin (x) cos (x)

d er i v a t i v e tan (ln (a x + b))

a re a y = 6 - 3 x^{2}, y = 3 x^{2}, x = - 2, x = 2