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Calculus Derivatives Power, Quotient, Chain Flashcards | StudBud
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Calculus Derivatives Power, Quotient, Chain
Calculus Derivatives Power, Quotient, Chain
10 terms
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StudBud Administration
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Project by Cordy McJunkins, Cameron Gammill, and Matthew Roberts #calculusab
Flashcards
10 cards
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Questions
10
Answers
1
If g(x)= sin
2
x, then what is g'(x) using the Chain Rule? Hint: sin
2
x = (sinx)
2
(sinx)2
2cosxsinx
-2sinxcosx
2cos2xsinx
2
find s'(
t
) using the Chain Rule: s(
t
)= (1/
t
-3)
2
-2/(t-3)3
2/(t-3)2
1/(t-3)3
-1/(t-2)3
3
Find
h'(
t
) using the Product Rule:
h
(
t
)= (2
t
-1)(2
t
+1)
8t +4
4t2 +1
8t
8t -4
4
FInd f'(x) using the Chain Rule: f(x)= sin
3
4x
3sin24xcos4x
6sin22xcos2x
12sin24xcos4x
12cos24xsin4x
5
If j(x)= f(x)/6, what is j'(x)? Hint: Think carefully and simply
6f'(x)/36
0
f'(x)/2
f'(x)/6
6
Find g'(x) using the Quotient Rule. g(x)=(x
2
-3)/(5x-4)
2x/5
10x2 -10/(10x2 +8)
-5x2 +18x +15/(5x+4)2
5x2 +8x +15/(5x+4)2
7
Find g'(x) using the Chain Rule: g(x)= (4x +3)
3
3(4x+3)2
12(4x +3)2
12(4x2 +3)
12x2 +9
8
Find f'(x) using Quotient Rule. f(x)= (x
2
-1)/(x
3
+3)
-x4 /(x3 +2)2
3x2 +6x/(x3 +3)2
x4 -3x2 -6x/(x3 +3)2
-x4 +3x2 +6x/(x3 +3)2
9
Find y' using the Quotient Rule. y=(5x -4)/(9x +3)
21/(9x-3)2
36/(9x2 +3)
45x/(5x-4)2
21/(9x-3)
10
Find f'(x) using the Product Rule. f(x)= (x
2
-1)(x+5)
3x2 + 10x +1
3x2 + 10x -1
2x2 + 7x -1
x2+ 5x +1
