For differentiating an expression, use the diff
command. Specify the expression
you want to differentiate, and the differentiation variable. Specifying
the differentiation variable is important even if your expression
contains only one variable. For example, find the derivative of an
expression with one variable:
diff(x^2 + sqrt(sin(x)), x)
Note:
If you do not specify differentiation variable, |
Find first-order partial derivatives of a multivariable expression by specifying differentiation variables:
diff(sin(x*cos(x*y)), x); diff(sin(x*cos(x*y)), y)
To take second and higher order derivatives, you can use nested
calls to the diff
function.
More efficiently, use only one diff
command and specify variables for
each differentiation step. Calling diff
only once is shorter and also can
improve performance because MuPAD^{®} internally converts nested
calls to diff
into
a single call with multiple arguments:
diff(diff(sqrt(sin(x)), x), x); diff(sqrt(sin(x)), x, x)
When computing higher order derivatives with respect to one variable, use the sequence operator as a shortcut:
diff(sqrt(sin(x)), x $ 3) = diff(sqrt(sin(x)), x, x, x)
To compute mixed derivatives, specify differentiation variables for each step:
diff(x*cos(x*y), y, x)
Note: To improve performance, MuPAD assumes that all mixed derivatives commute. For example, . |
This assumption suffices for most of engineering and scientific problems.