derivative (7x^2+6x)(7x-8)

Lösung

ableitung von

(7 x^{2} + 6 x) (7 x - 8)

147 x^{2} - 28 x - 48

Schritte zur Lösung

\frac{d}{d x} ((7 x^{2} + 6 x) (7 x - 8))

Wende die Produktregel an:

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

f = 7 x^{2} + 6 x, g = 7 x - 8

= \frac{d}{d x} (7 x^{2} + 6 x) (7 x - 8) + \frac{d}{d x} (7 x - 8) (7 x^{2} + 6 x)

\frac{d}{d x} (7 x^{2} + 6 x) = 14 x + 6

\frac{d}{d x} (7 x - 8) = 7

= (14 x + 6) (7 x - 8) + 7 (7 x^{2} + 6 x)

Vereinfache

(14 x + 6) (7 x - 8) + 7 (7 x^{2} + 6 x) : 147 x^{2} - 28 x - 48

= 147 x^{2} - 28 x - 48

d er i v a t i v e f (x) = x^{2} + 2 x

\frac{d}{d x} (\frac{x ^{2} + 6 x + 9}{x - 3})

d er i v a t i v e f (x) = (2 x - 5) (3 x + 1)

y^{^{'}} = \frac{x y ^{3}}{1 + x ^{2}}, y (0) = 1

\frac{\partial}{\partial x} (\frac{( 3 x - 4 y )}{- x + 6 y})