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Derivatives Sample Questions:

Question 1: Find .


Answer: 

Explanation: Apply the power rule.


 

Question 2: Find .


Answer: 

Explanation: Apply the power rule.


 

Question 3: Find .


Answer: 

Explanation: Apply the power rule.


 

Question 4: Let . Find 


Answer: 

Explanation: Apply the power rule.


 

Question 5: A tangent line is passing through and . Find the average rate of change at .


Answer: 

Explanation: Use the first principle of derivative.


 

Question 6: Let , find .


Answer: 

Explanation: Apply the quotient rule.


 

Question 7: Let , find at 


Answer: 

Explanation: Use the standard derivative of the trigonometric function.


 

Question 8: Calculate the average rate of change of on the interval .


Answer: 

Explanation: Use the average rate of change formula.


 

Question 9: Check if the following function is differentiable at ?



Answer: No

Explanation: Check the LHL, RHL, and the value of the function at .


 

Question 10: Find , if 


Answer: 

Explanation: Use the product rule.

 

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