Question

Find the derivative using the rules of differentiation written in simplest form please help!

Answer 1

Given:

`f(x)=tan(x)* ln(x)`

To Determine: The derivative of the given function

Solution

Using product rule

`\begin{gathered} f(x)=uv \\ f^(\prime)(x)=u(dv)/(dx)+v(du)/(dx) \end{gathered}`
`\begin{gathered} u=tanx \\ (du)/(dx)=sec^2x \\ v=lnx \\ (dv)/(dx)=(1)/(x) \end{gathered}`

Therefore

`f^(\prime)(x)=tanx*(1)/(x)+ln(x)* sec^2(x)`
`f^(\prime)(x)=ln(x)sec^2x+(tan(x))/(x)`