# Composition of two differentiable functions

## Homework Statement

Is the composition of two differentiable functions always differentiable?

E.x.

h(x) = sin(x)
k(x) = 1/x for x not equal 0

Does this automatically mean h(k(x)) is differentiable?

Thank you,

M

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Hurkyl
Staff Emeritus
Gold Member
Sure. You even know a formula for the derivative, right?

Fredrik
Staff Emeritus
Gold Member
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 $h\circ k$ or $x\mapsto h(k(x))$. (Note the special "mapsto" arrow).