Find the derivative of the function?

#y=ln tan^2 3x#

1 Answer
Mar 8, 2018

Answer:

#dy/dx=12csc(6x)#

Explanation:

We to find the derivative of

#y=ln(tan^2(3x))=2ln(tan(3x))#

Use the chain rule, if #y=f(u)# and #u=g(x)# then

#dy/dx=dy/(du)(du)/dx#

Let #y=2ln(u)=>(dy)/(du)=2/u#

and #u=tan(3x)=>(du)/(dx)=3sec^2(3x)#

Thus

#dy/dx=6/usec^2(3x)=6/tan(3x)sec^2(3x)=6csc(3x)sec(3x)#

Or by applying the identity #csc(2x)=1/2csc(x)sec(x)#

#dy/dx=12csc(6x)#