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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