# Composition of two differentiable functions

1. Apr 3, 2010

### michonamona

1. The problem statement, all variables and given/known data
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

2. Apr 3, 2010

### Hurkyl

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

3. Apr 3, 2010

### Fredrik

Staff Emeritus
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).

4. Apr 4, 2010

### michonamona

Thank you for your replies.

So the composition of two differentiable functions is ALWAYS differentiable? I know the derivative of their composition, we just use the chain rule.

Thanks Fredrik. I never thought about that. Now I understand why they always use LaTeX Code: h\\circ k when referring to composition of functions.

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