d/(dM)((R)(M^2(c/2-M/3)))

解答

\frac{d}{d M} ((R (M)) (M^{2} (\frac{c}{2} - \frac{M}{3})))

\frac{d R}{d M} M^{2} (\frac{c}{2} - \frac{M}{3}) + (c M - M^{2}) R

求解步骤

\frac{d}{d M} ((R) (M^{2} (\frac{c}{2} - \frac{M}{3})))

使用微分乘法定则:

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

f = R, g = M^{2} (\frac{c}{2} - \frac{M}{3})

= \frac{d R}{d M} M^{2} (\frac{c}{2} - \frac{M}{3}) + \frac{d}{d M} (M^{2} (\frac{c}{2} - \frac{M}{3})) R

\frac{d}{d M} (M^{2} (\frac{c}{2} - \frac{M}{3})) = c M - M^{2}

= \frac{d R}{d M} M^{2} (\frac{c}{2} - \frac{M}{3}) + (c M - M^{2}) R

e x p an d \frac{( 3 s + 8 )}{( s + 3 ) ^{2}}

e x p an d \frac{4 x ^{2} - 14 x - 30}{x ( x - 3 )}

e x p an d (x - \frac{31}{2})^{2} + x

e x p an d (t^{\frac{1}{2}} + t^{\frac{1}{3}})^{3}

\frac{d}{d t} ((X) (2 X (N - X)))