(\partial)/(\partial x)(xln(xy-5))

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = x, g = ln (x y - 5)

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

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

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

= 1 \cdot ln (x y - 5) + \frac{y}{y x - 5} x

Vereinfache

1 \cdot ln (x y - 5) + \frac{y}{y x - 5} x : ln (x y - 5) + \frac{x y}{x y - 5}

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

x \to 3 lim (x^{2} + 4)

\int_{- 1}^{1} x (1.5 x^{2}) d x

\frac{d}{d x} (ln (\frac{x + 1}{x - 1}))

\frac{d}{d x} (\frac{4}{( x ^{2} + 9 ) ^{3}})

d er i v a t i v e 2 cos (2 t)