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

Lösung

ableitung von

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

3 x^{2} - 10 x + 2

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

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

\frac{\partial}{\partial x} ((x + 1)^{2} + y^{2} - 1)

x \to 2 lim (\frac{x ^{2} + 2 x - 8}{3 x - 6})

\frac{d}{d x} (3 sin (x))

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

x \to 1 lim (\frac{I n ( x )}{x - 1})