(\partial)/(\partial x)(sqrt(x)+ln(5x+y))

Lösung

\frac{\partial}{\partial x} (x + ln (5 x + y))

\frac{1}{2 x} + \frac{5}{5 x + y}

Schritte zur Lösung

\frac{\partial}{\partial x} (x + ln (5 x + y))

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x) + \frac{\partial}{\partial x} (ln (5 x + y))

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

\frac{\partial}{\partial x} (ln (5 x + y)) = \frac{5}{5 x + y}

= \frac{1}{2 x} + \frac{5}{5 x + y}

\frac{\partial}{\partial y} (cos (2 x) y)

\int \frac{1}{y ^{4} y ^{2} - 5} d y

d er i v a t i v e ln (k x)

\int \frac{x}{1 + 6 x - 3 x ^{2}} d x

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