Question

How do you differentiate given `tan^2(x)`?

Answer 1

`d/dx[tan^2x]=2tanxsec^2x`.

Explanation:

The big idea here is that we are squaring something. The derivative of `x^2` is `2x`, so the derivative of `u` squared (`u` stands for any function) is `2u` * (the derivative of `u`).

This is by the chain rule.

In other words, `d/dx[u^2]=2u*d/dx[u]`.

So `d/dx[tan^2x]=2tanx*d/dx[tanx]`.

Remember that `d/dx[tanx]=sec^2x`, so our final answer is `d/dx[tan^2x]=2tanxsec^2x`.

If you don't remember why or how `d/dx[tanx]=sec^2x`, rewrite `tanx=sinx/cosx` and take the derivative using the quotient rule.

`d/dx[tanx]=d/dx[sinx/cosx]=(cos^2x-(-sin^2x))/cos^2x=1/cos^2x=sec^2x`