# Second Derivatives and Beyond

# Second Derivatives via Formulas Exercises

### Example 1

Find the second derivative of the function.

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

### Example 2

Find the second derivative of the function.

*f*(*x*) = 8*x*^{4} + 3*x*^{2} - 9*x*

### Example 3

Find the second derivative of the function.

*g*(*x*) = *x* + 7

### Example 4

Find the second derivative of the function.

*g*(*x*) = *ln* *x*

### Example 5

Find the second derivative of the function.

*h*(*x*) = 2^{x}

### Example 6

For the function, either find the second derivative or determine that the second derivative does not exist.

*f*(*x*) = *xe*^{x}

### Example 7

For the function, either find the second derivative or determine that the second derivative does not exist.

*f*(*x*) = 8

### Example 8

For the function, either find the second derivative or determine that the second derivative does not exist.

*f*(*x*) = *x*^{(5/3)}

### Example 9

*f*(*x*) = |*x*|

### Example 10

*f*(*x*) = *e*^{x}