(\partial)/(\partial x)(sqrt(x)(x-2))

Lösung

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

\frac{3 x - 2}{2 x}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = x - 2

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

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

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

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

Vereinfache

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

= \frac{3 x - 2}{2 x}

\int \frac{1}{x ( x + 1 )} d x

ma c l a u r in 2 x e^{x^{2}}

\int x^{3} e^{x y}

\int_{6}^{8} \frac{44}{( x - 6 ) ^{3}} d x

\frac{d}{d x} (- \frac{10}{x ^{3}})