If y= x log|x+√(1+x²)|-√(1+x²) then dy/dx=

d/dx{√(1+cos x)/sin x}=

If y={sin x/2 sin x²/2. Sin x³/2³...sin xⁿ/2ⁿ}then dy/dx=

If y=acos2x+b sin2x, then  y₂+4y=

d/dx{cos[2 sin^-1(cos x)]}=

If y=(ax+b/cx+d) then 2y₁y₃=

d/dx{Sin^-12x/1+x²+Sec^-11+x²/1-x²}=

The derivative of (ax+b)^cx+d w.r.to x is

If x=e^2tcos 3t, then d²x/dt² at t=π/2 is

If xy=c² then dy/dx=