# Derivatives

### Example 1

If *f*(*x*) = *x* + 3, find *f'*(1).

### Example 2

Translate each phrase into Leibniz Notation.

- the instantaneous rate of change of
*z*with respect to*x*when*x*= 5 - the instantaneous rate of change of
*x*with respect to*z*when*x*= 5 - the instantaneous rate of change of
*x*with respect to*z*when*z*= 5

### Example 3

Translate the Leibniz notation into words.

### Example 4

If *x* is measured in hours, *y* is measured in wombats, and *z* is measured in mice, determine the units of the quantity .

### Example 5

If *x* is measured in hours, *y* is measured in wombats, and *z* is measured in mice, determine the units of the quantity: .

### Example 6

*x* is measured in hours, *y* is measured in wombats, and *z* is measured in mice, determine the units of the quantity: .