# Computing Derivatives

### Example 1

What is the largest the slope of *f*(*x*) = sin(*x*) ever gets? The smallest?

### Example 2

What is the largest the slope of *f*(*x*) = cos(*x*) ever gets? The smallest?

### Example 3

Let *f*(*x*) = -sin(*x*). Based on the discussion in this section, what is a reasonable formula for *f'*(*x*)?

### Example 4

Let *f*(*x*) = -cos(*x*). Based on the discussion in this section, is a reasonable formula for *f'*(*x*)?

### Example 5

Find the derivative of the function. Be sure to use correct notation.

*f*(*x*) = sin(*x*)

### Example 6

Find the derivative of the function. Be sure to use correct notation.

*g*(*z*) = cos(*z*)

### Example 7

Find the derivative of the function. Be sure to use correct notation.

*h*(*y*) = -sin(*y*)

### Example 8

Find the derivative of the function. Be sure to use correct notation.

*r*(k) = -cos(*k*)