Question

dy/dx y=e^(tanx)/lnx

Answer 1

there is no avoiding the quotient rule for this one
\[\left(\frac{f}{g}\right)'=\frac{gf'-fg'}{g^2}\] with
\[f(x)=e^{\tan(x)}. f'(x)=\sec^2(x)e^{\tan(x)}, g(x)=\ln(x), g'(x)=\frac{1}{x}\] plug and play