- #1

- 122

- 0

## 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

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter michonamona
- Start date

- #1

- 122

- 0

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

Hurkyl

Staff Emeritus

Science Advisor

Gold Member

- 14,916

- 19

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

- #3

Fredrik

Staff Emeritus

Science Advisor

Gold Member

- 10,851

- 413

- #4

- 122

- 0

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

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

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).

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.

Share:

- Replies
- 7

- Views
- 692