4. dv/dy=-½(1-4cos(5y))^(-3/2)(20sin(5y)),
dv/dy=-10sin(5y)(1-4cos(5y))^(-3/2). Chain differentiation: let u=cos(5y), v=(1-4u)^-½. dv/dy=(dv/du)(du/dy).
5. dy/dx=½x²cos(x/2)+2xsin(x/2). Formula: d(uv)/dx=u(dv/dx)+v(du/dx) where u=x² and v=sin(x/2)
6. (Hard to read) y=x²cos²(-3x)? dy/dx=d(uv)/dx=u(dv/dx)+v(du/dx) where u=x² and v=z², z=cos(-3x), dv/dz=2z, dz/dx=3sin(-3x),
dv/dx=(dv/dz)(dz/dx)=2z(3sin(-3x))=6zsin(-3x)=6cos(-3x)sin(-3x).
dy/dx=6x²cos(-3x)sin(-3x)+2xcos²(-3x).
7. dy/dx=2sec(2x)tan(2x)+2sec²(2x).