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)=

If f(x)=x²+x²/(1+x²)+x²/(1+x²)²+...+x²/(1+x²)ⁿ+... then x=0

d/dx{1-cos 2x/3+2 sin 2x}=

If x= a(cos θ+θ sin θ), y=a(sin θ-θ cos θ)then dy/dx=

If sec θ-cos θ, y= secⁿ θ- cosⁿ θ then (dy/dx)²=

d/dx{Tan^-1 1/√x²-1}=

If x= a(θ+sin θ), y=a(1-cosθ) then d²y/dx² at θ=π/4 is