# How do you find the derivative of #y=tan^2(5x)# ?

##### 1 Answer

The derivative of tan2(5x) is 10tan(5x)sec2(5x).

#### Explanation:

The derivative of

Our function is the composite of three simpler functions:

Start with

Then find the tangent of that.

Finally, find the square of **that**.

So to find the derivative we need the threefold chain rule:

If

In our problem,

so

Thus

Note: You might prefer doing the problem by letting

Then

Many students prefer the second method, but occasionally you may encounter a problem for which the notation in the second method becomes ambiguous, so it is good to know both methods.