Question

$$(\frac{n^{1^{2}+m^{2}}}{n^{-1m}})^{1-m}\times(\frac{n^{m^{2}+n^{2}}}{n^{-mn}})^{m-n}\times(\frac{n^{2}+1^{2}}{n^{-n1}})^{n-1}$$

Differentiate w.r.t. n

$\frac{n^{m\left(m+1\right)}\left(n^{3}\ln(\left(n^{2}+1\right)n^{n_{1}})+n\ln(\left(n^{2}+1\right)n^{n_{1}})-3n^{5}\ln(n)-3n^{3}\ln(n)+n_{1}n^{3}-n^{5}-n_{1}n^{2}+nn_{1}+n^{3}-n^{2}-n_{1}+1\right)\left(\left(n^{2}+1\right)n^{n_{1}}\right)^{n-1}\left(n^{m^{2}+mn+n^{2}}\right)^{m-n}}{\left(n^{2}+1\right)\left(n^{m^{2}+m+1}\right)^{m}}$