Question

If f(x) = 3tan2x, find f'(pi/2)

Answer 1

Given the function f(x) defined as:

`f(x)=3\tan(2x)`

We need to find the derivative first. Using the chain rule, we know that:

`(\tan u)^(\prime)=u^(\prime)\cdot\sec²u`

Then, taking the derivative if u = 2x:

`\begin{gathered} f^(\prime)(x)=3(2)\sec²(2x) \\ \\ \Rightarrow f^(\prime)(x)=6\sec²(2x) \end{gathered}`

Using this result, we can evaluate the derivative at x = π/2:

`\begin{gathered} f^(\prime)((\pi)/(2))=6\sec²(2\cdot(\pi)/(2))=6\sec²(\pi)=6\cdot(-1)² \\ \\ \therefore f^(\prime)((\pi)/(2))=6 \end{gathered}`