<s>[INST] Simplifying partial derivative I have trouble understanding how this simplification was done. Can anyone explain please?
$\frac{\partial V}{\partial M}=\frac{5}{6}\frac{2^{1/3}3^{1/2}}{5^{5/6}}\frac{M^{-1/6}}{p_1^{1/3}p_2^{1/2}}=\frac{5^{1/6}}{2^{2/3}3^{1/2}p_1^{1/3}p_2^{1/2}}M^{-1/6}$
Thanks for your help.
Stan
 [/INST] Besides some rearrangements, all the simplification comes in the numeric terms through factorisation and applying exponent rules:
$\begin{eqnarray}\frac{5}{6} \frac{2^{1/3} 3^{1/2}}{5^{5/6}} & = & \frac{5}{2 \times 3} \frac{2^{1/3} 3^{1/2}}{5^{5/6}} \\
& = & \frac{5^{6/6}}{5^{1/6}}  \frac{2^{1/3}}{2^{3/3}} \frac{3^{1/2}}{3^{2/2}} \\
& = & 5^{5/6} \frac{1}{2^{2/3}} \frac{1}{3^{1/2}}\end{eqnarray}$
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