derivative 3(2ze^z+e^zz^2)

Lösung

ableitung von

3 (2 z e^{z} + e^{z} z^{2})

3 (e^{z} z^{2} + 4 e^{z} z + 2 e^{z})

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= 3 (2 (e^{z} + e^{z} z) + e^{z} z^{2} + 2 z e^{z})

Multipliziere aus

2 (e^{z} + e^{z} z) + e^{z} z^{2} + 2 z e^{z} : e^{z} z^{2} + 4 e^{z} z + 2 e^{z}

= 3 (e^{z} z^{2} + 4 e^{z} z + 2 e^{z})

d er i v a t i v e f (x) = (x - 4)^{2}

t an g e n t 9 + 5 x^{2}

\int_{0}^{R} \frac{1}{1 + x ^{2}} d x

\int \frac{( x - b )}{x} d x

\frac{\partial}{\partial x} (sin (x) e^{y x^{2}} x)