derivative (x^2+8)(5-x)

Lösung

ableitung von

(x^{2} + 8) (5 - x)

10 x - 3 x^{2} - 8

Schritte zur Lösung

\frac{d}{d x} ((x^{2} + 8) (5 - x))

Wende die Produktregel an:

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

f = x^{2} + 8, g = 5 - x

= \frac{d}{d x} (x^{2} + 8) (5 - x) + \frac{d}{d x} (5 - x) (x^{2} + 8)

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

\frac{d}{d x} (5 - x) = - 1

= 2 x (5 - x) + (- 1) (x^{2} + 8)

Vereinfache

2 x (5 - x) + (- 1) (x^{2} + 8) : 10 x - 3 x^{2} - 8

= 10 x - 3 x^{2} - 8

t an g e n t f (x) = \frac{- 8 x}{x ^{2} + 1}, (- 1, 4)

\int \frac{tan ( x )}{csc ( x ) + cot ( x )} d x

\frac{d}{d x} (4 x^{5} + 2 x^{3} + 6 x^{2} + 3 x)

\int 8 e^{2 θ} sin (2 θ) d θ

y^{^{'}} + y = x \cdot e^{- x} + 1