derivative-(3(z^2+1))/(z^2)

Lösung

ableitung von

- \frac{3 ( z ^{2} + 1 )}{z ^{2}}

\frac{6}{z ^{3}}

Schritte zur Lösung

\frac{d}{d z} (- \frac{3 ( z ^{2} + 1 )}{z ^{2}})

Entferne die Konstante:

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

= - 3 \frac{d}{d z} (\frac{z ^{2} + 1}{z ^{2}})

Wende die Quotientenregel an:

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

= - 3 \cdot \frac{\frac{d}{d z} ( z ^{2} + 1 ) z ^{2} - \frac{d}{d z} ( z ^{2} ) ( z ^{2} + 1 )}{( z ^{2} ) ^{2}}

\frac{d}{d z} (z^{2} + 1) = 2 z

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

= - 3 \cdot \frac{2 z z ^{2} - 2 z ( z ^{2} + 1 )}{( z ^{2} ) ^{2}}

Vereinfache

- 3 \cdot \frac{2 z z ^{2} - 2 z ( z ^{2} + 1 )}{( z ^{2} ) ^{2}} : \frac{6}{z ^{3}}

= \frac{6}{z ^{3}}

a re a y^{2} = 6 - x, 3 y = x + 12

\int_{π}^{2 π} 9 x sin (x) d x

n = 0 \sum \infty 12 \cdot 626582

\int \frac{2 + e ^{x}}{e ^{x}} d x

n = 1 \sum \infty \frac{7}{2 ^{n - 1}}