Let the function FX be differentiable at point X and find the following limit. Limf (x + α h) - f (x - β h) / h, (α, β are constants)
lim(h→0)[f(x+αh)-f(x-βh)]/h = lim(h→0)[f(x+αh)-f(x)]/h + lim(h→0)[f(x)-f(x-βh)]/h = α*lim(h→0)[f(x+αh)-f(x)]/(αh) + β*lim(h→0)[f(x-βh)-f(x)]/(-βh) = α*f'(x) + β*f'(x) = ...