Question

How do you take the derivative of `tan3x`?

Answer 1

Use the chain rule and the fact that the derivative of the tangent function is the square of the secant function.

Explanation:

I recommend memorizing this:
`d/dx(tanx) =sec^2 x`

Applying the chain rule, we get

`d/dx(tanu) = (sec^2 u) * (du)/dx`

In this problem, we have `u = 3x`, so `(du)/dx = 3`

Now we put these pieces together to see that the derivative of `tan 3x` is

`d/dx(tan 3x) = (sec 3x ) * 3`, which is more clear if we write it as:

`d/dx(tan 3x) = 3sec 3x`