# High School Math : General Derivatives and Rules

## Example Questions

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### Example Question #1 : Finding Derivative At A Point

Find  if the function  is given by

Explanation:

To find the derivative at , we first take the derivative of . By the derivative rule for logarithms,

Plugging in , we get

### Example Question #2 : Finding Derivative At A Point

Find the derivative of the following function at the point .

Explanation:

Use the power rule on each term of the polynomial to get the derivative,

Now we plug in

### Example Question #11 : Derivatives

Let . What is ?

Explanation:

We need to find the first derivative of f(x). This will require us to apply both the Product and Chain Rules. When we apply the Product Rule, we obtain:

In order to find the derivative of , we will need to employ the Chain Rule.

We can factor out a 2x to make this a little nicer to look at.

Now we must evaluate the derivative when x = .

### Example Question #1 : Finding Derivatives

What is the first derivative of ?

Explanation:

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.

### Example Question #2 : General Derivatives And Rules

Explanation:

This problem is best solved by using 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.

### Example Question #3 : General Derivatives And Rules

Give the average rate of change of the function  on the interval  .

Explanation:

The average rate of change of  on interval  is

Substitute:

### Example Question #1 : Concept Of The Derivative

What is the derivative of ?

Explanation:

To solve this problem, 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.

### Example Question #2 : Derivative Defined As The Limit Of The Difference Quotient

What is the derivative of ?

Explanation:

To solve this problem, 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.

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

That means this problem will look like this:

Notice that , as anything times zero is zero.

Remember, anything to the zero power is one.

### Example Question #2 : Finding Derivatives

What is the derivative of ?

Explanation:

To solve this problem, 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.

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

Notice that , as anything times zero is zero.

### Example Question #2 : General Derivatives And Rules

What is the derivative of ?

Explanation:

To get , we can use the power rule.

Since the exponent of the  is , as , we lower the exponent by one and then multiply the coefficient by that original exponent:

Anything to the  power is .

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