(\partial)/(\partial x)((x-2)(x^2+4))

Lösung

\frac{\partial}{\partial x} ((x - 2) (x^{2} + 4))

3 x^{2} - 4 x + 4

Schritte zur Lösung

\frac{\partial}{\partial x} ((x - 2) (x^{2} + 4))

Wende die Produktregel an:

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

f = x - 2, g = x^{2} + 4

= \frac{\partial}{\partial x} (x - 2) (x^{2} + 4) + \frac{\partial}{\partial x} (x^{2} + 4) (x - 2)

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

\frac{\partial}{\partial x} (x^{2} + 4) = 2 x

= 1 \cdot (x^{2} + 4) + 2 x (x - 2)

Vereinfache

1 \cdot (x^{2} + 4) + 2 x (x - 2) : 3 x^{2} - 4 x + 4

= 3 x^{2} - 4 x + 4

x v^{'} + v = - \frac{4 - v + v ^{2}}{1 - v + 4 v ^{2}}

\int \frac{64 + x ^{2}}{x} d x

h \to 0 lim (\frac{( 3 ^{h} - 1 )}{h})

y^{^{'}} = 8 + t - y

d er i v a t i v e 3^{s i n (x)}