How do you find the derivative of #y=tan^2(5x)# ?
The derivative of tan2(5x) is 10tan(5x)sec2(5x).
The derivative of
Our function is the composite of three simpler functions:
Then find the tangent of that.
Finally, find the square of that.
So to find the derivative we need the threefold chain rule:
In our problem,
Note: You might prefer doing the problem by letting
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.