DIFFERENTIATE
Syntax
DIFFERENTIATE ( equation|expression, symbol, expression)
Implemented in iMath since version 2.2.0 or earlier.
Explanation
Differentiate the expression or both sides of the equation with respect to the symbol. The third parameter gives the number of times to differentiate.
If you are differentiating a function, e.g. DIFFERENTIATE(f(x), x, 1), iMath will create a derivative object. This looks like a fraction with a differential in the numerator and another in the denominator. If you need to cancel a term in this fraction, you must use the simplification "cancel-diff".
You might be tempted to create a differential of a function manually with something like differential(f) over differential(x). This is not the recommended way, though, because in complicated terms iMath might not be able to match the correct differentials in numerator and denominator, which can lead to strange results for higher-order derivatives and when printing.
It is possible to differentiate to a symbol that is a function.
Example
FUNCTION { {none}, T, x}
@eq1@ EQDEF q = -k A DIFFERENTIATE( T,x,1 )
@eq2@ EQDEF SIMPLIFY(@eq1@ * differential(x), "canceldiff")
This defines the equation for heat conduction and prepares it for integration by separation of the variables.