d/(d{x)}(({x}ln(({x)/y)/({z)})}{{z}})

Lösung

\frac{d}{d x} (\frac{x ln ( \frac{x y}{z} )}{z})

\frac{ln ( \frac{x y}{z} ) + 1}{z}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ln ( \frac{x y}{z} )}{z})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{z} \frac{d}{d x} (x ln (\frac{x y}{z}))

Wende die Produktregel an:

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

f = x, g = ln (\frac{x y}{z})

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

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

\frac{d}{d x} (ln (\frac{x y}{z})) = \frac{1}{x}

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

Vereinfache

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

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

x d y - (y + y) d x = 0, y (1) = 1

\int \frac{x}{x ^{4} + 1} d x

d er i v a t i v e - \frac{4}{3} x^{- \frac{5}{2}}

\int x^{3} - 3 x + 4 x - 5 d x

n = 0 \sum \infty 3^{n} 8^{- n + 1}