derivative of (x-5*ln(x/5))

Lösung

\frac{d}{d x} ((x - 5) \cdot ln (\frac{x}{5}))

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

Schritte zur Lösung

\frac{d}{d x} ((x - 5) ln (\frac{x}{5}))

Wende die Produktregel an:

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

f = x - 5, g = ln (\frac{x}{5})

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

\frac{d}{d x} (x - 5) = 1

\frac{d}{d x} (ln (\frac{x}{5})) = \frac{1}{x}

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

Vereinfache

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

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

\frac{d}{d x} (- \frac{375}{x ^{4}})

\int_{- 2}^{3} x^{2} - x - 6 d x

x \to 6 lim (x + 2)

d er i v a t i v e (343 + x)^{- \frac{1}{3}}

\frac{d}{d x} (2 x + 7)