Advanced Derivatives Quiz: Tricky Calculus Challenges!
Test your derivative mastery with 8 medium-difficulty questions. 4-second timer per question – share your score for viral fun! Bold colors and clear answers await.
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Quiz Questions & Answers
Review every prompt, the correct responses, and helpful context to prep for your own run-through.
Question 1: What is the derivative of f(x) = sin(3x) using the chain rule? (Definition focus)
-3 sin(3x)
3 cos(3x)
cos(3x)
3 sin(3x)
Question 2: For f(x) = x^2 * e^x, apply the product rule to find f'(x). (Application focus)
x^2 e^x
2x + x^2
2x e^x
2x e^x + x^2 e^x
Question 3: If y = x / (x+1), what's y' using the quotient rule? (Framework application)
(x+1 - x) / (x+1)^2
1 / (x+1)^2
-1 / (x+1)^2
1 / (x+1)
Question 4: In implicit differentiation for x^2 + y^2 = 25, what's dy/dx at (3,4)? (Scenario evaluation)
-3/4
4/3
-4/3
3/4
Question 5: For related rates: If V = (4/3)πr^3 and dr/dt = 2, what's dV/dt when r=3? (Consequence focus)
144π
24π
72π
36π
Question 6: Myth bust: Is the derivative of a constant function always zero? (Myth busting)
No, it's undefined
No, it depends on x
No, it's 1
Yes
Question 7: Using L'Hôpital's rule for lim x->0 sin(x)/x? (Advanced application)
1 (derivatives: cos(x)/1)
Undefined
0
∞
Question 8: What's the second derivative of f(x) = x^3 indicating? (Consequence/mindset focus)
Acceleration constant
Slope only
Maximum point
Concavity (f''(x) = 6x)