Expert: Paul Klarreich - 10/8/2010

Question
if y = tan^3 (3x), what is ((d^2)y)/(d(x^2)) * (pi/12)?

I have tried to evaluate it by finding the derivative of the first part: y = tan^3
(3x) but I'm not sure what to do with the whole mess of the second part.

Answer
Questioner:   Christie
Country:  United States
Category:  Advanced Math
Private:  No
 
Subject:  Calculus
Question:  if y = tan^3 (3x), what is ((d^2)y)/(d(x^2)) * (pi/12)?

I have tried to evaluate it by finding the derivative of the first part: y = tan^3(3x) but I'm not sure what to do with the whole mess of the second part.
......................................

y = tan^3(3x)

y' = 9 tan^2(3x) sec^2(3x)

Now that is a product.  Sorry about that, but you will have to deal with the 'whole mess':

y'' = 27 [tan^2(3x) 2 sec(3x) sec(3x) tan(3x) PLUS

sec^2(3x) 2 tan(3x) sec^2(3x) ]

= 54 [tan^3() sec^2() + tan() sec^4()]

Now use  3x = pi/4 in there and you should be able to finish.