What is the d/(dM)(-M+1/8 ra) ?

The d/(dM)(-M+1/8 ra) is -1+(a(dr)/(dM))/8

What is the first d/(dM)(-M+1/8 ra) ?

The first d/(dM)(-M+1/8 ra) is -1+(a(dr)/(dM))/8

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\frac{d}{d M} (- M + \frac{1}{8} r (M) a)

- 1 + \frac{a \frac{d r}{d M}}{8}

Solution steps

\frac{d}{d M} (- M + \frac{1}{8} r a)

Simplify

- M + \frac{1}{8} r a : - M + \frac{a r}{8}

= \frac{d}{d M} (- M + \frac{a r}{8})

Apply the Sum/Difference Rule:

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

= - \frac{d M}{d M} + \frac{d}{d M} (\frac{a r}{8})

\frac{d M}{d M} = 1

\frac{d}{d M} (\frac{a r}{8}) = \frac{a \frac{d r}{d M}}{8}

= - 1 + \frac{a \frac{d r}{d M}}{8}

What is the d/(dM)(-M+1/8 ra) ?
The d/(dM)(-M+1/8 ra) is -1+(a(dr)/(dM))/8
What is the first d/(dM)(-M+1/8 ra) ?
The first d/(dM)(-M+1/8 ra) is -1+(a(dr)/(dM))/8