derivative 10z^2e^z

解答

导数

10 z^{2} e^{z}

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

求解步骤

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

将常数提出:

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

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

使用微分乘法定则:

(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})

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