diff
diff
('expression','variable','order') - Differentiate.
If the 'order' is omitted, the first order derivative is assumed.
The function is used to perform symbolic or numeric derivatives. It can be inserted by typing
diff(
or from the
Function
palette under
Derivative
template (this is simpler).
Chose the
Derivative
template and insert in the 'variable' placeholder
x
and in the 'expression' placeholder
x
^{2}
. After that press
CTRL+.
(symbolic calculation). You should obtain this result:
We could have defined the 'expression'
f
first in variable
x
and
y
, for instance:
and found the first derivatives over the variables (partial derivatives, actually):
How to obtain the higher order derivatives? Press comma after the 'variable' and in the obtained placeholder insert the 'order' (integer). Here are the second derivatives:
Here are mixed derivatives as well:
Instead of an expression we could have defined a function and repeat the procedure:
Numerical derivatives are found at the given values. For instance:
Very important SMath feature is ability to find the
derivatives
over the
elements of a vector (matrix)
. Here is an example of finding Jacobi matrix and Jacobian: