Finding Second Derivative of a Function

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Math › Finding Second Derivative of a Function

Questions 1 - 10
1

What is the second derivative of ?

Explanation

To find the second derivative, we need to start by finding the first derivative.

To find the first derivative for this problem, we can use the power rule. The power rule states that we lower the exponent of each of the variables by one and multiply by that original exponent.

Remember that anything to the zero power is one.

Now we repeat the process, but we use as our expression.

For this problem, we're going to say that since, as stated before, anything to the zero power is one.

Notice that as anything times zero is zero.

2

What is the second derivative of ?

Explanation

To take the second derivative, we need to start with the first derivative.

To take the derivative of this equation, we can use the power rule. The power rule says that we lower the exponent of each variable by one and multiply that number by the original exponent.

Simplify.

Remember that anything to the zero power is equal to one.

Now we repeat the process, but using as our expression.

We're going to treat as being since anything to the zero power is equal to one.

Notice that since anything times zero is zero.

3

What is the second derivative of ?

Explanation

To find the second derivative, we need to start by finding the first derivative.

To find the first derivative, we can use the power rule. To do that, we lower the exponent on the variables by one and multiply by the original exponent.

We're going to treat as since anything to the zero power is one.

Notice that since anything times zero is zero.

Now we repeat the process but using as our expression.

Remember, anything to the zero power is one.

4

What is the second derivative of ?

Explanation

To find the second derivative, first we need to start with the first derivative.

To find the first derivative, we can use the power rule. We lower the exponent on all the variables by one and multiply by the original variable.

Anything to the zero power is one.

Now we repeat the process using as our expression.

We're going to treat as .

Notice that since anything times zero is zero.

As stated before, anything to the zero power is one.

5

If , what is ?

Explanation

The question is asking us for the second derivative of the equation. First, we need to find the first derivative.

To do that, we can use the power rule. To use the power rule, we lower the exponent on the variable and multiply by that exponent.

We're going to treat as since anything to the zero power is one.

Notice that since anything times zero is zero.

Now we do the exact same process but using as our expression.

As stated earlier, anything to the zero power is one.

6

What is the second derivative of ?

Explanation

To get the second derivative, first we need to find the first derivative.

To do that, we can use the power rule. That means we lower the exponent of the variable by one and multiply the variable by that original exponent.

Remember that anything to the zero power is one.

Now we do the same process again, but using as our expression:

Notice that , as anything times zero will be zero.

Anything to the zero power is one.

7

Define .

What is ?

Explanation

Rewrite:

Take the derivative of , then take the derivative of .

8

Define .

What is ?

Explanation

Take the derivative of , then take the derivative of .

9

What is the second derivative of ?

Explanation

To find the second derivative, we need to find the first derivative first. To find the first derivative, we can use the power rule.

For each variable, multiply by the exponent and reduce the exponent by one:

Treat as since anything to the zero power is one.

Remember, anything times zero is zero.

Now follow the same process but for .

Therefore the second derivative will be the line .

10

What is the second derivative of ?

Undefined

Explanation

To find the second derivative, first we need to find the first derivative.

To do that, we can use the power rule. To use the power rule, we lower the exponent on the variable and multiply by that exponent.

We're going to treat as since anything to the zero power is one.

Notice that since anything times zero is zero.

That leaves us with .

Simplify.

As stated earlier, anything to the zero power is one, leaving us with:

Now we can repeat the process using or as our equation.

As pointed out before, anything times zero is zero, meaning that .

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