# Derivatives

### Example 1

Using the limit definition, find *f'*(0) if *f*(*x*) = *x*^{2}.

### Example 2

Using the limit definition, find *f*'(-1) if *f*(*x*) = 1 - *x*^{2}.

### Example 3

Using the limit definition, let *f*(*x*) = *x*^{3}. Find *f'*(1).

### Example 4

If it exists, use the limit definition to find the derivative of *f*'(-1) if *f*(*x*) = *x*^{2}-* x.
*

### Example 5

Use the limit definition to find the derivative, if it exists: *f'*(*1*) where .

### Example 6

Use the limit definition to find the derivative, if it exists: *f'*(*0*) where *.*

### Example 7

Use the limit definition to find the derivative, if it exists: *f'*(*0*) where *f*(*x*) = *x*^{1/3}.