The first multiple choice quiz in this section is designed for those new to calculus. If you choose the wrong answer, you will get feedback about probable mistakes and a link to the correct rule to use as well as a step-by-step solution.
The second quiz is more extensive and is designed for you to use as a final test of your understanding of the principles presented in this section.
Take the derivative of the following functions, and calculate the value of the slope when x is equal to 1:
1.
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answer |
comments |
links |
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a. |
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correct |
rule:y=constant |
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b. |
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incorrect |
rule:y=constant |
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c. |
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incorrect |
rule: y=linear function |
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d. |
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incorrect |
rule:y=constant |
| Solution to 1: |
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2. 
| answer |
comments |
links |
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| a. |
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correct |
rule: y = polynomial rule: y = sum/difference |
| b. |
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incorrect subtract 1 from original power |
rule: y = polynomial |
| c. |
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incorrect don't forget coefficients |
rule: y = polynomial |
| d. |
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incorrect drop constants, drop variables with power of 1 |
rule: y = polynomial |
| Solution to 2: |
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3. 
| answer |
comments |
links |
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| a. |
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correct |
rule: y = sum/difference |
| b. |
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incorrect watch sign of second term |
rule: y = sum/difference |
| c. |
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incorrect signs must be consistent with original problem |
rule: y = sum/difference |
| d. |
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incorrect subtract 1 from powers in each term |
rule: y = polynomial |
| Solution to 3: |
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4. 
| answer |
comments |
links |
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| a. |
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correct |
y=product rule |
| b. |
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incorrect use product rule, not just multiply individual derivatives |
y=product rule |
| c. |
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incorrect add terms for product rule, not subtract |
y=product rule |
| d. |
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incorrect use product rule, not just add derivatives |
y=product rule |
| Solution to 4: |
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5. 
| answer |
comments |
links |
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| a. |
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correct |
y=quotient rule |
| b. |
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incorrect Denominator is g squared |
y=quotient rule |
| c. |
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incorrect subtract terms in numerator, not add |
y=quotient rule |
| d. |
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incorrect use quotient rule, not product rule |
y=quotient rule y=product rule |
| Solution to 5: |
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6. 
| answer |
comments |
links |
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| a. |
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correct |
y=composite fn/chain rule or y=gen'l power fn rule |
| b. |
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incorrect take derivative of inside term also |
y=gen'l power fn rule |
| c. |
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incorrect carry coefficients from inside derivative |
y=gen'l power fn rule y=polynomial rule |
| d. |
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incorrect derivatives have to be functions of x, last step is to sub value of u back into function |
y=composite fn/chain rule |
| Solution to 6: |
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7. 
| answer |
comments |
links |
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| a. |
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correct |
y=exponential function rule |
| b. |
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incorrect take derivative of power of e |
y=exponential function rule |
| c. |
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incorrect bring derivative down as coefficient |
y=exponential function rule |
| d. |
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incorrect multiply terms, not add |
y=exponential function rule |
| Solution to 7: |
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8. 
| answer |
comments |
links |
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| a. |
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correct |
y=natural log fn rule |
| b. |
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incorrect deriv of ln is reciprocal of term |
y=natural log fn rule |
| c. |
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incorrect drop ln symbol when take deriv |
y=natural log fn rule |
| d. |
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incorrect need deriv of term inside ln operation |
y=natural log fn rule |
| Solution to 8: |
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1. Find the formula for the slope of the following function:
| a. |
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correct |
| b. |
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incorrect |
| c. |
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incorrect |
| d. |
|
incorrect |
2 Find the formula for the slope of the following function
| a. |
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correct |
| b. |
|
incorrect |
| c. |
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incorrect |
| d. |
|
incorrect |
3. Find the formula for the slope of the following function:
| a. |
|
correct |
| b. |
|
incorrect |
| c. |
|
incorrect |
| d. |
|
incorrect |
4. Find the formula for the slope of the following function
| a. |
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correct |
| b. |
|
incorrect |
| c. |
|
incorrect |
| d. |
|
incorrect |
5. Find the formula for the slope of the following function
| a. |
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correct |
| b. |
|
incorrect |
| c. |
|
incorrect |
| d. |
|
incorrect |
6. Determine the slope and the rate of change of the slope of the following function when x=1:
| a. |
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correct |
| b. |
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incorrect |
| c. |
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incorrect |
| d. |
|
incorrect |
7. Use the product rule and the exponent rule to find the derivative of the function:
| a. |
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correct |
| b. |
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incorrect |
| c. |
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incorrect |
| d. |
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incorrect |
8. Although you can always simplify before using differentiation techniques, for practice use the exponent rule and the generalized power rule before simplifying to find the formula for the slope of the following function:
| a. |
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correct |
| b. |
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incorrect |
| c. |
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incorrect |
| d. |
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incorrect |
9. In the following function determine the value of the function, the slope, and the rate of change of the slope when x=-1.
| a. |
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correct |
| b. |
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incorrect |
| c. |
|
incorrect |
| d. |
|
incorrect |
[Index]
