If y=2 Tan^-1(x√2/1-x²)+log(1+x√2+x²/1-x√2+x²), then dy/dx=

If (x+y)²=ax² +by² then dy/dx=

If y√1+x²=log(x+√1+x²) then  (1+x²)y₁+xy=

If y=x+1/(x+1/x+....∞) then dy/dx=

If x= sin t cos 2t, y= cos t sin 2t then (dy/dx)_t=π/4

If x²+5xy+y²-2x+y-6=0 then y’’ at (-1,1) is

A function f:R→R satisfies the equation f(x+y)=f(x)f(y),x,y ε R and f(x)≠0 for any x εR. If f is differentiable at x=o and f^'(0)=2 then for any x εR, f¹(x)=

d/dx{x²+3x+6/(x+3)(x-5)}=

If x= acos³θ, y= asin³θ then d²y/dx² at θ=π/4 is

If sin θ. Sin (2α+θ).sin(4α+θ)+...+sin(2nα+θ)= sin nθ/2^n-1 where 2nα=π, then cot θ+cot(2α+θ)+...+cot(2nα+θ)=