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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.