Differentiate the function y = cos(sin(2x))?

To differentiate this function you will need the chain rule - differentiating what's inside the brackets and multiplying it by differentiating what's outside the brackets. In this case sin(2x) goes to 2cos(2x) and cos(sin(2x)) goes to - sin(sin(2x)). Therefore dy/dx = -2cos(2x)sin(sin2x)