## Create Symbolic Functions

Symbolic functions represent math functions. Use symbolic functions for differentiation, integration, solving ODEs, and other math operations. Create symbolic functions by using `syms`.

Note

Symbolic functions must be functions of symbolic variables. The Symbolic Math Toolbox™ currently does not support composite symbolic functions, or symbolic functions that are functions of another symbolic functions.

Create a symbolic function `f` with variables `x` and `y` by using `syms`. Creating `f` automatically creates `x` and `y`.

`syms f(x,y)`

Assign a mathematical expression to `f`.

`f(x,y) = x^2*y`
```f(x, y) = x^2*y```

Find the value of `f` at `(3,2)`.

`f(3,2)`
```ans = 18```

Symbolic functions accept array inputs. Calculate `f` for multiple values of `x` and `y`.

```xVal = 1:5; yVal = 3:7; f(xVal,yVal)```
```ans = [ 3, 16, 45, 96, 175]```

You can differentiate symbolic functions, integrate or simplify them, substitute their arguments with values, and perform other mathematical operations. For example, find the derivative of `f(x,y)` with respect to `x`. The result `dfx` is also a symbolic function.

`dfx = diff(f,x)`
```dfx(x,y) = 2*x*y```

Calculate `df(x,y)` at `x = y + 1`.

`dfx(y+1,y)`
```ans = 2*y*(y + 1)```

If you are creating a constant function, such as `f(x,y) = 1`, you must first create `f(x,y)`. If you do not create `f(x,y)`, then the assignment `f(x,y) = 1` throws an error.