What is the d/(dM)((R(M,C))(M^2(C/2-M/3))) ?

The d/(dM)((R(M,C))(M^2(C/2-M/3))) is d/(dM)({R}(M,C))M^2(C/2-M/3)+(CM-M^2){R}(M,C)

What is the first d/(dM)((R(M,C))(M^2(C/2-M/3))) ?

The first d/(dM)((R(M,C))(M^2(C/2-M/3))) is d/(dM)({R}(M,C))M^2(C/2-M/3)+(CM-M^2){R}(M,C)

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

\frac{d}{d M} (R (M, C)) M^{2} (\frac{C}{2} - \frac{M}{3}) + (CM - M^{2}) R (M, C)

Solution steps

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

Treat

C

as a constant

Apply the Product Rule:

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

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

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

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

= \frac{d}{d M} (R (M, C)) M^{2} (\frac{C}{2} - \frac{M}{3}) + (CM - M^{2}) R (M, C)

6 (7 + 11)

x (x - x)

(csc (x) + cot (x))^{2}

(2 - cos^{2} (x)) (cos^{2} (x))

What is the d/(dM)((R(M,C))(M^2(C/2-M/3))) ?
The d/(dM)((R(M,C))(M^2(C/2-M/3))) is d/(dM)({R}(M,C))M^2(C/2-M/3)+(CM-M^2){R}(M,C)
What is the first d/(dM)((R(M,C))(M^2(C/2-M/3))) ?
The first d/(dM)((R(M,C))(M^2(C/2-M/3))) is d/(dM)({R}(M,C))M^2(C/2-M/3)+(CM-M^2){R}(M,C)