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

Lösung

ableitung von

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

\frac{- 3 z - 12}{2 z ^{3} z + 3}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = z + 3, g = \frac{1}{z ^{2}}

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

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

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

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

Vereinfache

\frac{1}{2 z + 3} \cdot \frac{1}{z ^{2}} + (- \frac{2}{z ^{3}}) z + 3 : \frac{- 3 z - 12}{2 z ^{3} z + 3}

= \frac{- 3 z - 12}{2 z ^{3} z + 3}

\frac{d y}{d x} + y tan (x) = 2 x cos (x)

\frac{\partial}{\partial z} (x y + yz + x z)

\int \frac{1}{3} x^{3} d x

\int_{0}^{1} \frac{6}{1 - x ^{2}} d x

\frac{\partial}{\partial x} (arcsin (\frac{x}{l}))