Question

Use the principle of logarithmic differentiation, where appropriate, to find the derivative of the following function.

Answer 1

\[f(x)= \tan([\ln(x)]^x)\]

Answer 2

let f(x) be Y
\[y=\tan (\ln x)^{x}\]

\[\tan^{-1} y=(lnx)^{x}\]

Answer 3

\[\ln \tan^{-1} y=xln(lnx)\]

Answer 4

taking derivative

\[(\frac{1}{\tan^{-1} y})*(\frac{1}{1+y^{2}})*\frac{dy}{dx}=x(\frac{1}{lnx})(\frac{1}{x})+lnlnx\]

Answer 5

solve for dy/dx