# Limit Definition Of A Derivative

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This quiz will test your knowledge of the limit definition of a derivative. You are to answer the questions to the best of your ability, and submit your answers no later than one week after the first lesson on the limit definition of a derivative.

• 1.

• 2.

• 3.

### What is the derivative of x^2?

• A.

X^2

• B.

2x

• C.

2x^2

B. 2x
Explanation
The derivative of a function represents its rate of change at any given point. In this case, the function is x^2. To find its derivative, we can apply the power rule of differentiation. According to the power rule, when we differentiate x^n, the result is n*x^(n-1). Applying this rule to x^2, we get 2*x^(2-1), which simplifies to 2x. Therefore, the derivative of x^2 is 2x.

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• 4.

### What is the derivative of x^4+3 at x=2?

• A.

32

• B.

4

• C.

12

• D.

3

A. 32
Explanation
The derivative of a function represents the rate of change of the function at a given point. To find the derivative of x^4+3, we can apply the power rule, which states that the derivative of x^n is equal to n*x^(n-1). Applying this rule, the derivative of x^4 is 4*x^(4-1) = 4*x^3. Since we are interested in finding the derivative at x=2, we substitute x=2 into the derivative expression: 4*2^3 = 4*8 = 32. Therefore, the derivative of x^4+3 at x=2 is 32.

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• 5.

### Set up the limit to find the derivative of x^6+x^4+(x+3)^(1/2).  DO NOT SOLVE.

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• Current Version
• Mar 20, 2023
Quiz Edited by
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• Oct 15, 2010
Quiz Created by
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