# Differentiation question

1. Jul 29, 2007

### jetsetjoe

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

Show that there exists a differentiable real function:

(f(x))^5 + f(x) + x = 0

2. Relevant equations
??
definition of the derivative: lim (as x -> a) [f(x) - f(a)]/x-a

3. The attempt at a solution

Not really sure where to start with this one. any help would be appreciated.

2. Jul 30, 2007

### CompuChip

By (f(x))^5, did you mean the fifth power $f^5(x) = (f(x))^5[/tex] or the fifth derivative [itex]f^{(5)}(x) = \frac{d^5f(x)}{dx^5}$. In the first case it's not a differential equation at all and I don't see why you need the definition for derivative.

Please clarify what you mean exactly, and we'll give you a push in the right direction.