The derivative of (sin x)^x _w.r.to x is

If |x|<1 then d/dx[1+px/q+p(p+q)/2!(x/q)²+p(p+q)(p+2q)/3! (x/q)³+...]

Let f(x)=1/|x| for |x| ≤1, f(x)=ax²+b for |x|>1. If f is differentiable at any point, then

The derivative of Tan^-1√(1+x²)-1/x w.r.to Tan^-12x√(1-x²)/(1-2x²) at x=0 is

If cos x/2 . cos x/2². Cos x/2³.... cos x/2ⁿ= sin x/2ⁿsin (x/2ⁿ) then (1/2²)sec²x/2+(1/2⁴) sec²x/2²...(1/2²ⁿ)sec²x/2ⁿ=

If ax²+2hxy+by²=1 then (hx+by)³y₂=

d/dx{Tan^-1(acos x-bsin x/b cos x+a sin x)}=

If sin² mx+cos² ny=a² then dy/dx=

If x=sin^-1t, y= √(1-t²) then d²y/dx²=

The derivative of cos hx/2w.r.to x is