The second derivative is the derivative of the first derivative function.

With our original function, 

We may find the first derivative to be: 

Note that the chain rule was used to find the first derivative.

Now to find the second derivative we must take the derivative of this function:

To find the area under a curve, you need to use an integral expression. The number at the base of your integral sign is your lower bound (the smaller x-value that defines one vertical edge of your area), which in this case is 3. The number at the top of your integral sign is your upper-bound (the larger x-value that defines the other vertical edge of your area), which in this case is 100. The equation that goes inside of your integral expression is the same equation that you were initially given, without the "y = ". Finally, you need to add "dx" after your equation in order to complete it.

To find the area under a curve, you need to use an integral expression. The number at the base of your integral sign is your lower bound (the smaller x-value that defines one vertical edge of your area), which in this case is 4. The number at the top of your integral sign is your upper-bound (the larger x-value that defines the other vertical edge of your area), which in this case is 12. The equation that goes inside of your integral expression is the same equation that you were initially given, without the "y = ". Finally, you need to add "dx" after your equation in order to complete it.

To find the area under a curve, you need to use an integral expression. The number at the base of your integral sign is your lower bound (the smaller x-value that defines one vertical edge of your area), which in this case is 2. The number at the top of your integral sign is your upper-bound (the larger x-value that defines the other vertical edge of your area), which in this case is 6. The equation that goes inside of your integral expression is the same equation that you were initially given, without the "y = ". Finally, you need to add "dx" after your equation in order to complete it.

To find the area under a curve, you need to use an integral expression. The number at the base of your integral sign is your lower bound (the smaller x-value that defines one vertical edge of your area), which in this case is 5. The number at the top of your integral sign is your upper-bound (the larger x-value that defines the other vertical edge of your area), which in this case is 8. The equation that goes inside of your integral expression is the same equation that you were initially given, without the "y = ". Finally, you need to add "dx" after your equation in order to complete it.

To solve, you must first differentiate according to the power rule and then plug in 1. Thus,

Power rule:

Since for all values of x, the first derivative is 6, our answer is 6.

This problem is asking you to find the indefinite integral of the given function, f'(x). To do this, we need to work through the function one term at a time. For each term in the function, we perform two steps. First, we divide the coefficient of that term by (n+1), where "n" is the value of the exponent for that term's x-value. Second, we add 1 to the value of that term's x-value. We continue this process for each term in the function. 

So, for , this would look like

which when integrated will equal 

You must remember to include "C" in your final answer; this acts as a placeholder for any constants that may have been present in the original equation.

This problem is asking you to find the indefinite integral of the given function, f'(x). To do this, we need to work through the function one term at a time. For each term in the function, we perform two steps. First, we divide the coefficient of that term by (n+1), where "n" is the value of the exponent for that term's x-value. Second, we add 1 to the value of that term's x-value. We continue this process for each term in the function. 

So, for , this would look like

which when integrated will equal 

You must remember to include "C" in your final answer; this acts as a placeholder for any constants that may have been present in the original equation.

This problem is asking you to find the indefinite integral of the given function, f'(x). To do this, we need to work through the function one term at a time. For each term in the function, we perform two steps. First, we divide the coefficient of that term by (n+1), where "n" is the value of the exponent for that term's x-value. Second, we add 1 to the value of that term's x-value. We continue this process for each term in the function. 

So, for , this would look like

which when integrated will equal 

You must remember to include "C" in your final answer; this acts as a placeholder for any constants that may have been present in the original equation.

This problem is asking you to find the indefinite integral of the given function, f'(x). To do this, we need to work through the function one term at a time. For each term in the function, we perform two steps. First, we divide the coefficient of that term by (n+1), where "n" is the value of the exponent for that term's x-value. Second, we add 1 to the value of that term's x-value. We continue this process for each term in the function. 

So, for , this would look like

which when integrated will equal 

You must remember to include "C" in your final answer; this acts as a placeholder for any constants that may have been present in the original equation.