Question

$$\frac{ 729 { n }^{ 2 } \pm { p }^{ 4 } }{ 81n- { p }^{ 2 } }$$

Evaluate

$\frac{729n^{2}±p^{4}}{81n-p^{2}}$

Differentiate w.r.t. n

$\frac{-p^{2}\frac{\mathrm{d}}{\mathrm{d}n}(729n^{2}±p^{4})+81n\frac{\mathrm{d}}{\mathrm{d}n}(729n^{2}±p^{4})-81\left(729n^{2}±p^{4}\right)}{\left(81n-p^{2}\right)^{2}}$