#[1]" "d/dx(3cos2x+sin^2x)#
Sum rule: #d/dx[f(x)+g(x)]=d/dx[f(x)]+d/dx[g(x)]#
Multiplication by constant: #d/dx[c*f(x)]=c*d/dx[f(x)]#
#[2]" "=3*d/dx(cos2x)+d/dx(sin^2x)#
The derivative of #cos(x)# is #-sin(x)#. You can use that here, but you will have to use chain rule.
#[3]" "=3*(-sin2x)*d/dx(2x)+d/dx(sin^2x)#
The derivative of #2x# is only #2#.
#[4]" "=3*(-sin2x)*2+d/dx(sin^2x)#
You can use power rule on #sin^2x#, but you will have to use chain rule as well.
#[5]" "=-6sin2x+2*d/dx(sinx)#
The derivative of #sin(x)# is #cos(x).
#[6]" "=-6sin2x+(2sinx)*(cosx)#
#[7]" "=color(blue)(2sinxcosx-6sin2x)#
