AP Calculus AB Unit 3 — Differentiation ‒ Composite, Implicit, and Inverse Functions Practice Test
AP Calculus AB Unit 3 — Differentiation ‒ Composite, Implicit, and Inverse Functions Practice Test
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Question 1 of 19
1. Question
If x^{ 3} + y^{ 3} =6xy , find the derivative through implicit differentiation
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Question 2 of 19
2. Question
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Question 3 of 19
3. Question
f(x)=6^{5x27x} find the derivated
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Question 4 of 19
4. Question
f ( x )= ( 4 x^{3} − 9 x ^{2} +4 x − 8)^{2} Using the chain rule for derivatives, find f ‘ ( x ).
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Question 5 of 19
5. Question
Find the derivative of the function of the circle x^{2} + y^{2} =25
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Question 6 of 19
6. Question
Find the derivative of the function lny=ln x^{ 6}
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Question 7 of 19
7. Question
f ( x )=sin ( x ^{2} ) . Find f ( x ) f ‘ ( x )
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Question 8 of 19
8. Question
Find the derivative of the exponential function,y=e^{sec 3 θ}
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Question 9 of 19
9. Question
Let f and g be inverse functions. The following table lists a few values of f , g , and f ‘ find g ‘ ( 2 ).
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Question 10 of 19
10. Question
Let g ( x ) =3 −2 x − x ^{3} and let f be the inverse function of g . Notice that g ( 1 )=0 . Find f ‘ ( 0 ) .
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Question 11 of 19
11. Question
Given f ( x )=arctan ( 3 x ) , find f ‘ ( x ) .
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Question 12 of 19
12. Question
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Question 13 of 19
13. Question
g ( x ) =x ( 5 x ^{4} +7 x ^{3} − x+ 6 ) How would you rewrite g(x) so it can be differentiated using the power rule?
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Question 14 of 19
14. Question
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Question 15 of 19
15. Question
f ( x )=arctan ( 3 x ) . Find f ‘ ( x ) .
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Question 16 of 19
16. Question
How many derivatives can you take of a function?
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Question 17 of 19
17. Question
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Question 18 of 19
18. Question
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Question 19 of 19
19. Question
Find f ‘ ‘ ‘ ( x ) when f ( x )=10 x ^{5} + 3 x^{ 4} − 5 x ^{3} +2 x^{ 2} −10 x +6
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