# How to define the derivative of a function

Hello,

I want to tell Sage what expression to use for the derivative of a funtion *a*. This vould be something like this: *diff(a,t) = b^2*. But this doesn't do the trick...

**Example**
I want to define this set of differential quations:

- aDot = da/dt = b^2,
- bdot = db/da = u.

I want Sage to find the relation between *a* and *u*. For that Sage needs to differentiate *a* twice:
- diff(a,t,2)
But to be able to calculate d^2/d *t* ^2 *a* = d/d*t *b*^2 = 2 *bu*, Sage needs to to both differential equations.

How can I implemant that?

Thanks alot in advance for your replies!

Johannes

It sounds like the following might work for you: http://doc.sagemath.org/html/en/refer...