Question

Find dy/dx if y=sin^2 x

Answer 1

use the chain rule

Answer 2

y = sin^2 x
y ' = 2 sin(x) (sin(x))' = 2 sin(x) cos(x)

it could be simplied again, by using the identity :
sin(2x) = 2 sin(x)cos(x)

so,
y ' = 2 sin(x) cos(x) = sin(2x)

Answer 3

does that make sense ?

Answer 4

Alternatively, you could write

y=sin^2(x) as y=sin(x)*sin(x)

and use the Product Rule:

y' = cos(x)*sin(x) + sin(x)*cos(x) = 2sin(x)cos(x) = sin(2x),

which is (of course) the same answer as RadEn's!