derivative of ln(3x+5y)

Lösung

\frac{d}{d x} (ln (3 x + 5 y))

\frac{3 + 5 \frac{d y}{d x}}{3 x + 5 y}

Schritte zur Lösung

\frac{d}{d x} (ln (3 x + 5 y))

Wende die Kettenregel an:

\frac{1}{3 x + 5 y} \frac{d}{d x} (3 x + 5 y)

= \frac{1}{3 x + 5 y} \frac{d}{d x} (3 x + 5 y)

\frac{d}{d x} (3 x + 5 y) = 3 + 5 \frac{d y}{d x}

= \frac{1}{3 x + 5 y} (3 + 5 \frac{d y}{d x})

Vereinfache

\frac{1}{3 x + 5 y} (3 + 5 \frac{d y}{d x}) : \frac{3 + 5 \frac{d y}{d x}}{3 x + 5 y}

= \frac{3 + 5 \frac{d y}{d x}}{3 x + 5 y}

\frac{d}{d x} (\frac{1}{4 x - 7})

x \to 0 + lim ((1 + tan (x))^{\frac{3}{x}})

\frac{d}{d x} (arcsin (x) + 1 - x^{2})

d er i v a t i v e f (x) = e^{x} - x^{4}

n = 1 \sum \infty ln (\frac{n}{2 n + 5})