Given that ${y = \tan^{-1}(3^x)}$, find an expression of \({\frac{\mathrm{d}y}{\mathrm{d}x}}\

Question

Given that ${y = \tan^{-1}(3^x)}$, find an expression of ${\frac{\mathrm{d}y}{\mathrm{d}x}}$.

Accepted Answer

$\frac{{{3}^{x}}\ln 3}{1+{{3}^{2x}}}$

Techniques of Differentiation - Derivatives of Inverse Trigonometric Functions