d/(dh)((pih^2)/3 (3sqrt(6)-h))

解答

\frac{d}{d h} (\frac{π h ^{2}}{3} (36 - h))

πh (- h + 26)

求解步骤

\frac{d}{d h} (\frac{π h ^{2}}{3} (36 - h))

将常数提出:

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

= \frac{π}{3} \frac{d}{d h} (h^{2} (36 - h))

使用微分乘法定则:

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

f = h^{2}, g = 36 - h

= \frac{π}{3} (\frac{d}{d h} (h^{2}) (36 - h) + \frac{d}{d h} (36 - h) h^{2})

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

\frac{d}{d h} (36 - h) = - 1

= \frac{π}{3} (2 h (36 - h) + (- 1) h^{2})

化简

\frac{π}{3} (2 h (36 - h) + (- 1) h^{2}) : πh (- h + 26)

= πh (- h + 26)

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