Precalculus : Find the First Derivative of a Function

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #132 : Introductory Calculus

Find the first derivative of the following function:

Possible Answers:

Correct answer:

Explanation:

To solve, simply differentiate using the power rule for differentiation as outline below.

Thus,

Notice that our constant term disappeared because the derivative of a constant is zero.

Simplifying the above equation, we get:

Thus, our answer is:

Example Question #41 : Find The First Derivative Of A Function

Find the first derivative of the following equation:

Possible Answers:

Correct answer:

Explanation:

To solve, simply use the power rule as outline below:

Power rule:

Thus,

Example Question #134 : Introductory Calculus

Find the first derivative of the following function:

Possible Answers:

Correct answer:

Explanation:

To solve, you must use the product rule as outline below.

Product rule:

Thus,

Distribute the 2x and 2.

Combine like terms to simplify.

Example Question #758 : Pre Calculus

Find the first derivative of the function  .

Possible Answers:

Correct answer:

Explanation:

An equivalent form of writing    is   . The derivative of an exponential power  is , so the derivative of  is , or .

Example Question #759 : Pre Calculus

Find the first derivative: 

Possible Answers:

None of the other answers.

Correct answer:

Explanation:

Simplify first:

Use the power rule on each term:

Power rule:

Note that constants become zero.

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