derivative f(x)=(2x-sqrt(x))(5x+2)

Lösung

ableitung von

f (x) = (2 x - x) (5 x + 2)

\frac{- 15 x + 40 x x - 2}{2 x} + 4

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = 2 x - x, g = 5 x + 2

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

\frac{d}{d x} (2 x - x) = 2 - \frac{1}{2 x}

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

= (2 - \frac{1}{2 x}) (5 x + 2) + 5 (2 x - x)

Vereinfache

(2 - \frac{1}{2 x}) (5 x + 2) + 5 (2 x - x) : \frac{- 15 x + 40 x x - 2}{2 x} + 4

= \frac{- 15 x + 40 x x - 2}{2 x} + 4

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

x y^{^{'}} + y + y^{2} = 0

f^{^{'}} (x) = (x + 1)^{2} \cdot (x - 2)^{3} \cdot (2 x + 3)

\int x cos (x) sin (x) d x

x \to 2 lim (ln (4 - x^{2}))