# AP Calculus AB : Derivatives

## Example Questions

### Example Question #75 : Derivatives Of Functions

Find the limit of the function below using L'Hopital's rule

Explanation:

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STEPS

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Given:

Plug in 4 for q to test to use L'Hopital's rule

From this indeterminate form, realize we can now use L'Hopital's rule, deriving the expressions in the numerator and denominator independently of one another

(pi comes from chain rule with qpi)

Thus, we arrive at our correct answer:

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### Example Question #91 : Derivatives

Find the derivative of the function:

Explanation:

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STEPS

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Given:

Understand the derivative of a^x:

Thus:

We find the chain by deriving the compound operation "2r"

Plug 2 in for the chain:

Thus, we arrive at the correct answer:

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### Example Question #92 : Derivatives

Find the derivative of the function:

Explanation:

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STEPS

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Given:

Now, take the derivative of x^2, and plug in for the "chain"

Multiplying, we arrive at the correct answer

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### Example Question #78 : Derivatives Of Functions

Find the limit of the function below using L'Hopital's Rule

The limit does not exist

Explanation:

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STEPS

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Given:

Try the limit. Plug in two for y and check the result:

Thus, we realize me must use L'Hopital's Rule on the original quotient, deriving the expressions in the numerator and denominator independently

Try the limit once more:

Simplifying the numerator, we arrive at the correct answer:

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### Example Question #93 : Derivatives

Find the derivative of the function

,

where  is a constant.

Explanation:

The derivative of the function is equal to

and was found using the following rules:

### Example Question #94 : Derivatives

Find the derivative of the function:

Explanation:

The derivative of the function is equal to

and was found using the following rules:

### Example Question #95 : Derivatives

Find the derivative of the function:

Explanation:

The derivative of the function is equal to

and was found using the following rules:

### Example Question #96 : Derivatives

Find the derivative of the following function:

Explanation:

The derivative of the function is equal to

and was found using the following rules:

The derivative was simplified from

to its most simple form.

### Example Question #97 : Derivatives

Find the derivative of the function:

Explanation:

The derivative of the function is equal to

and was found using the following rules:

### Example Question #98 : Derivatives

Find the derivative of the function: