Question

How do you use the product rule to differentiate `y=cos(x)*sin(x)` ?

Answer 1

`y=u*v=cos(x)*sin(x)`

`u'=-sin(x)`

`v'=cos(x)`

`y'=(uv)'=u'v+uv'=-sin(x)*sin(x)+cos(x)*cos(x)`

`y'=(uv)'=u'v+uv'=-sin^2(x)+cos^2(x)`