d/(dL)((q)((L/4+({K}(q,L))/2)q^3))

解答

\frac{d}{d L} ((q) ((\frac{L}{4} + \frac{K ( q , L )}{2}) q^{3}))

q q^{3} (\frac{1}{4} + \frac{1}{2} \frac{d}{d L} (K (q, L)))

求解步骤

\frac{d}{d L} ((q) ((\frac{L}{4} + \frac{K ( q , L )}{2}) q^{3}))

将

q

视为常数

将常数提出:

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

= q q^{3} \frac{d}{d L} (\frac{L}{4} + \frac{K ( q , L )}{2})

使用微分加减法定则:

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

= q q^{3} (\frac{d}{d L} (\frac{L}{4}) + \frac{d}{d L} (\frac{K ( q , L )}{2}))

\frac{d}{d L} (\frac{L}{4}) = \frac{1}{4}

\frac{d}{d L} (\frac{K ( q , L )}{2}) = \frac{1}{2} \frac{d}{d L} (K (q, L))

= q q^{3} (\frac{1}{4} + \frac{1}{2} \frac{d}{d L} (K (q, L)))

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