### All High School Math Resources

## Example Questions

### Example Question #4 : Derivative Defined As The Limit Of The Difference Quotient

**Possible Answers:**

**Correct answer:**

To solve this equation, 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.

### Example Question #5 : Derivative Defined As The Limit Of The Difference Quotient

What is the derivative of ?

**Possible Answers:**

**Correct answer:**

To solve this equation, 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:

### Example Question #6 : Derivative Defined As The Limit Of The Difference Quotient

What is the derivative of ?

**Possible Answers:**

**Correct answer:**

To solve this equation, 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.

Just like it was mentioned earlier, anything to the zero power is one.

### Example Question #7 : Derivative Defined As The Limit Of The Difference Quotient

What is the derivative of ?

**Possible Answers:**

**Correct answer:**

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.

### Example Question #8 : Derivative Defined As The Limit Of The Difference Quotient

What is the derivative of ?

**Possible Answers:**

**Correct answer:**

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.

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

Notice that since anything times zero is zero.

Simplify.

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

### Example Question #9 : Derivative Defined As The Limit Of The Difference Quotient

What is the derivative of ?

**Possible Answers:**

**Correct answer:**

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.

### Example Question #10 : Derivative Defined As The Limit Of The Difference Quotient

What is the derivative of ?

**Possible Answers:**

**Correct answer:**

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.

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

For this problem that would look like this:

Notice that since anything times zero is zero.

### Example Question #31 : Calculus I — Derivatives

What is the derivative of ?

**Possible Answers:**

**Correct answer:**

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.

### Example Question #11 : Finding Derivatives

**Possible Answers:**

**Correct answer:**

To find the derivative of the problem, we can use the power rule. The power rule says to multiply the coefficient of the variable by the exponent of the variable and then lower the exponent value by one.

To make that work, we're going to treat as , since anything to the zero power is one.

This means that is the same as .

Now use the power rule:

Anything times zero is zero.

### Example Question #12 : Finding Derivatives

What is the first derivative of ?

**Possible Answers:**

**Correct answer:**

To find the derivative of , we can use the power rule.

The power rule states that we multiply each variable by its current exponent and then lower the exponent of each variable by one.

Since , we're going to treat as .

Anything times zero is zero, so our final term , regardless of the power of the exponent.

Simplify what we have.

Our final solution, then, is .