# Chain rule for differentiation

From Calculus

## Statement for two functions

Suppose and are functions such that is differentiable at a point , and is differentiable at . Then the composite is differentiable at , and we have:

In terms of general expressions:

In point-free notation, we have:

where denotes the pointwise product of functions.

## Related rules

- Chain rule for higher derivatives
- Product rule for differentiation
- Product rule for higher derivatives
- Differentiation is linear
- Inverse function theorem (gives formula for derivative of inverse function).