Calc Question Please Help?

Question

How do u find the derivative of r= tan^2(3-x)?

If u can please show me step by step cuz i keep getting the wrong answer. I know it involves Chain Rule or something but i jus dont kno how to do it. Thanks!

Answer 1

It's a bit simpler if you work with the identity
tan^2(a) = 1+ 1/cos^2(a)=f(a)

In fact if you let (3-x)= a, then da/dx=-1, and....
d(tan^2(a))= d f(a)/da*da/dx

Answer 2

r=tan^2(3-x)
dr/dx=2tan(3-x)sec^2(3-x)(-1)
=-2tan(3-x)sec^2(3-x)