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Derivatives
Robert
Marık
createdusin
gA
croTE X
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Mendel University Brno
Derivatives – the chain rule
Robert Marık
You will differentiate composite functions.
• Full screen button or CTRL+L switshes between window and FullScreen mode.
• Start button gives you a random problem.
• Hint button shows you a hint.
• Solution button shows you a solution.
• Next question button shows another random problem.
• Home button moves here.
c© 2006 [email protected] Revision Date: September 28, 2006 Version 1.0
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Question
Find y′ for y = (3x − 1)6.
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Question
Find y′ for y = e−x.
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Question
Find y′ for y = e1−x2
.
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Question
Find y′ for y = e4x−1.
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Question
Find y′ for y = ln(1 − x).
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Question
Find y′ for y = (x + 3)−3.
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Question
Find y′ for y = ln(sin x).
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Question
Find y′ for y = sin(2x).
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Question
Find y′ for y = sin2 x.
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Question
Find y′ for y = cos3(2x).
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Question
Find y′ for y = sin(ex).
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Question
Find y′ for y = sin(ln x).
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Question
Find y′ for y = arctg(x2).
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Question
Find y′ for y = arctg1
x.
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Question
Find y′ for y = ln(x2 − 1).
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Question
Find y′ for y = arcsin√
x.
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Question
Find y′ for y = arctg√
x.
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Question
Find y′ for y = arctg x2.
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Question
Find y′ for y = arctg2 x.
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Question
Find y′ for y = tg 3x.
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Question
Find y′ for y = tg ln x.
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Question
Find y′ for y = tg3 x.
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Answer
y′ =((3x − 1)6)′ = 18(3x − 1)5
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Answer
y′ =(e−x
)′= −e−x
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Answer
y′ =(e1−x2
)′= −2xe1−x2
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Answer
y′ =(e4x−1)′ = 4e4x−1
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Answer
y′ = (ln(1 − x))′ = − 1
1 − x
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Answer
y′ =((x + 3)−3)′ = −3(x + 3)−4
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Answer
y′ = (ln(sin x))′ =cos x
sin x
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Answer
y′ = (sin(2x))′ = 2 cos(2x)
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Answer
y′ =(sin2 x
)′= 2 sin x cos x
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Answer
y′ =(cos3(2x)
)′= −6 cos2(2x) sin(2x)
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Answer
y′ = (sin(ex))′ = ex cos(ex)
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Answer
y′ = (sin(ln x))′ =cos(ln x)
x
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Answer
y′ =(arctg(x2)
)′=
2x
1 + x4
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Answer
y′ =
(arctg
1
x
)′=
1
1 +( 1
x
)2 ·(− 1
x2
)
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Answer
y′ =(ln(x2 − 1)
)′=
2x
x2 − 1
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Answer
y′ =(arcsin
√x)′
=1√
1 − x
1
2
1√x
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Answer
y′ =(arctg
√x)′
=1
1 + x
1
2
1√x
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Answer
y′ =(arctg x2)′ =
1
1 + x42x
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Answer
y′ =(arctg2 x
)′= 2
arctg x
1 + x2
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
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Answer
y′ = (tg 3x)′ =3
cos2 3x
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
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Answer
y′ = (tg ln x)′ =1
x cos2 ln x
Derivatives
Robert
Marık
createdusin
gA
croTE X
Hint
Solution
Next question
Home
Answer
y′ =(tg3 x
)′= 3 tg2 x
1
cos2 x