Is the composition of two differentiable functions always differentiable?
h(x) = sin(x)
k(x) = 1/x for x not equal 0
Does this automatically mean h(k(x)) is differentiable?
Sure. You even know a formula for the derivative, right?
I'll just comment about one of my little pet peeves. h(k(x)) is a number, not a function. The function you have in mind is written as LaTeX Code: h\\circ k or LaTeX Code: x\\mapsto h(k(x)) . (Note the special "mapsto" arrow).