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Popular >

d/(dm)(({r}(m))(m^2(c/2-m/3)))

Solution

\frac{d}{d m} ((r (m)) (m^{2} (\frac{c}{2} - \frac{m}{3})))

Solution

\frac{d}{d m} (r (m)) m^{2} (\frac{c}{2} - \frac{m}{3}) + (c m - m^{2}) r (m)

Solution steps

\frac{d}{d m} ((r (m)) (m^{2} (\frac{c}{2} - \frac{m}{3})))

Apply the Product Rule:

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

f = r (m), g = m^{2} (\frac{c}{2} - \frac{m}{3})

= \frac{d}{d m} (r (m)) m^{2} (\frac{c}{2} - \frac{m}{3}) + \frac{d}{d m} (m^{2} (\frac{c}{2} - \frac{m}{3})) r (m)

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

= \frac{d}{d m} (r (m)) m^{2} (\frac{c}{2} - \frac{m}{3}) + (c m - m^{2}) r (m)

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Frequently Asked Questions (FAQ)

What is the d/(dm)(({r}(m))(m^2(c/2-m/3))) ?
The d/(dm)(({r}(m))(m^2(c/2-m/3))) is d/(dm)({r}(m))m^2(c/2-m/3)+(cm-m^2){r}(m)
What is the first d/(dm)(({r}(m))(m^2(c/2-m/3))) ?
The first d/(dm)(({r}(m))(m^2(c/2-m/3))) is d/(dm)({r}(m))m^2(c/2-m/3)+(cm-m^2){r}(m)