Question

Differentiate
ln sin 2x

(Show all steps :)

Answer 1

Let t= 2x.

so we have dt/dx = 2 -------- (1)

Now y= sint
dy/dx = d(sint)/dx
= cost . dt/dx
using eq (1)
dy/dx = 2cos t
= 2cos2x

Answer 2

as the diff: of lnx is 1/x therefore ln sin2x will be \[(1/\sin2x) (\cos2x)2 = 2\cos2x/\sin2x = 2\cot2x \]