# Chain rule facts for kids

In differential calculus, the **chain rule** is a way of finding the derivative of a function. It is used where the function is within another function. This is called a composite function.

More specifically, if equals the composite function of the form:

where *g* is a function differentiable at *x* and *f* is a function differentiable at *g*(*x*), then the derivative of , written as , exists, and is equal to

- .

## Steps

**1.** Find the derivative of the outside function (all of it at once).

**2.** Find the derivative of the inside function (the bit between the brackets).

**3.** Multiply the answer from the first step by the answer from the second step. This is basically the last step in solving for the derivative of a function.

For example,

In this example, the cubed sign (^{3}) is the outside function and is the inside function. The derivative of the outside function would be , where *x* is replaced by the inside function. The derivative of the inside function would be 2*x*, which is multiplied by to get .

## Related pages

- Product rule

## See also

In Spanish: Regla de la cadena para niños

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