Derivative?

Find the derivative of \5xtan^2\(3x)

1 Answer
Jun 27, 2017

Use the product rule and the chain rule.

Explanation:

u = 5x, so u' = 5

v = tan^2(3x) = (tan(3x))^2 has derivative

v' = 2tan(3x) * d/dx(tan(3x))

= 2tan(3x) [sec^2(3x) * d/dx(3x)]

= 2tan(3x) sec^2(3x) * 3

= 6tan(3x) sec^2(3x)

d/dx(uv) = u'v+uv'

= [5][tan^2(3x)] + [5x][6tan(3x) sec^2(3x)]

= 5tan^2(3x) + 30 x tan(3x) sec^2(3x)

You may remove the common factors if you like.

= 5tan(3x)[tan(3x)+6xsec^2(3x)]