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Beliebt Rechnen >

derivative f(x)=(6x+7)(7x-8)

Lösung

ableitung von

f (x) = (6 x + 7) (7 x - 8)

Lösung

84 x + 1

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = 6 x + 7, g = 7 x - 8

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

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

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

= 6 (7 x - 8) + 7 (6 x + 7)

Vereinfache

6 (7 x - 8) + 7 (6 x + 7) : 84 x + 1

= 84 x + 1

Graph

Beliebte Beispiele

integral of 10sin(5x)

\int 10 sin (5 x) d x

integral of (1+2x^2)^2

\int (1 + 2 x^{2})^{2} d x

(dy)/(dx)=(2x)/(1+2y),y(2)=1

\frac{d y}{d x} = \frac{2 x}{1 + 2 y}, y (2) = 1

(2x)/y dx-(x^2)/(y^2)dy=0

\frac{2 x}{y} d x - \frac{x ^{2}}{y ^{2}} d y = 0

derivative f(x)=(2x)/7+1

d er i v a t i v e f (x) = \frac{2 x}{7} + 1