derivative of (3x/(x^2))

Lösung

\frac{d}{d x} (\frac{3 x}{x ^{2}})

- \frac{3}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x}{x ^{2}})

Entferne die Konstante:

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

= 3 \frac{d}{d x} (\frac{x}{x ^{2}})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= 3 \cdot \frac{\frac{d x}{d x} x ^{2} - \frac{d}{d x} ( x ^{2} ) x}{( x ^{2} ) ^{2}}

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

\frac{d}{d x} (x^{2}) = 2 x

= 3 \cdot \frac{1 \cdot x ^{2} - 2 xx}{( x ^{2} ) ^{2}}

Vereinfache

3 \cdot \frac{1 \cdot x ^{2} - 2 xx}{( x ^{2} ) ^{2}} : - \frac{3}{x ^{2}}

= - \frac{3}{x ^{2}}

x \to 0 lim (2^{x} + 6)

a re a e^{2 x}, e^{x}, [0, 1]

x \to - \infty lim (x + 7)

x \to 7 + lim (\frac{x + 1}{7 - x})

n = 1 \sum \infty \frac{6}{5 ^{n - 1}}