(\partial)/(\partial x)(xy+2x-ln(x^2y))

Lösung

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

y + 2 - \frac{2}{x}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial x} (x y) = y

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

\frac{\partial}{\partial x} (ln (x^{2} y)) = \frac{2}{x}

= y + 2 - \frac{2}{x}

\int (x^{2} + 3) d x

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

\int (4 x)^{2} d x

\int_{4}^{8} t^{2} ln (3 t) d t

\int \frac{1}{6 x ( 3 + x )} d x