Given:
[tex]f(x)=tan(x)\times ln(x)[/tex]
To Determine: The derivative of the given function
Solution
Using product rule
[tex]\begin{gathered} f(x)=uv \\ f^{\prime}(x)=u\frac{dv}{dx}+v\frac{du}{dx} \end{gathered}[/tex][tex]\begin{gathered} u=tanx \\ \frac{du}{dx}=sec^2x \\ v=lnx \\ \frac{dv}{dx}=\frac{1}{x} \end{gathered}[/tex]
Therefore
[tex]f^{\prime}(x)=tanx\times\frac{1}{x}+ln(x)\times sec^2(x)[/tex][tex]f^{\prime}(x)=ln(x)sec^2x+\frac{tan(x)}{x}[/tex]
