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Beliebt Rechnen >

derivative 10z^2e^z

Lösung

ableitung von

10 z^{2} e^{z}

Lösung

10 (2 z e^{z} + e^{z} z^{2})

Schritte zur Lösung

\frac{d}{d z} (10 z^{2} e^{z})

Entferne die Konstante:

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

= 10 \frac{d}{d z} (z^{2} e^{z})

Wende die Produktregel an:

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

f = z^{2}, g = e^{z}

= 10 (\frac{d}{d z} (z^{2}) e^{z} + \frac{d}{d z} (e^{z}) z^{2})

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

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

= 10 (2 z e^{z} + e^{z} z^{2})

Graph

Beliebte Beispiele

derivative ln(x^3)

d er i v a t i v e ln (x^{3})

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\frac{d}{d x} (a x^{3} + b x^{2} - \frac{c}{3} x + d)

derivative y=x^2(x-1)

d er i v a t i v e y = x^{2} (x - 1)

(\partial)/(\partial x)(x^7y^9-x^6y^8)

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integral of 1/((x^2+x+1))

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