If y= a cos x+(b+2x)sinx then y₂+y=

d/dx{√(1+sin x/1-sin x)}=

If y²=4ax then 4a(1+y₁²)^3/2+(y²+4a²)^3/2y₂=

If y=(1+x²)Tan^-1x then y₂=

If r²=x²+y²,x=e^t sin t,y=e^t cos t then dr/dt=

If ‘f’ is differentiable function, f(1)=0, f¹(1)=3/5 and y=f(e^2x)e^x then (dy/dx)_x=0 =

d/dx{sin^-1(3x-4x³)}=

d/dx{Tan^-1(x/1-√1-x²)}=

The derivative of a^xlog x+(x²-1) sin x w.r.t x is

If xy(x+y)=2 then dy/dx=