(\partial)/(\partial x)(xln(xy))

Lösung

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

ln (x y) + 1

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = x, g = ln (x y)

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

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

\frac{\partial}{\partial x} (ln (x y)) = \frac{1}{x}

= 1 \cdot ln (x y) + \frac{1}{x} x

Vereinfache

1 \cdot ln (x y) + \frac{1}{x} x : ln (x y) + 1

= ln (x y) + 1

\int \frac{4}{x ^{2} + 9} d x

y^{^{''}} - 4 y^{^{'}} + 4 y = 6 t^{2} e^{2 t}

d er i v a t i v e f (x) = ln (e x)

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

\frac{\partial}{\partial x} (arcsin (\frac{a}{b} sin (x)))