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## Differentiate Expressions

MuPAD® notebooks will be removed in a future release. Use MATLAB® live scripts instead.

MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.

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)`
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### Note

If you do not specify differentiation variable, `diff`(`expr`) returns the expression `expr`.

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)```
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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)```
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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)`
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To compute mixed derivatives, specify differentiation variables for each step:

`diff(x*cos(x*y), y, x)`
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### Note

To improve performance, MuPAD assumes that all mixed derivatives commute. For example, .

This assumption suffices for most of engineering and scientific problems.

#### Mathematical Modeling with Symbolic Math Toolbox

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