Derivatives

Robert

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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 marik@mendelu.czLast Revision Date: September 28, 2006 Version 1.0

Derivatives

Robert

Marık

createdusin

gA

croTE X

Hint

Solution

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Question

Find y′ for y = (3x − 1)6.

Derivatives

Robert

Marık

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Solution

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Question

Find y′ for y = e−x.

Derivatives

Robert

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Question

Find y′ for y = e1−x2

.

Derivatives

Robert

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Question

Find y′ for y = e4x−1.

Derivatives

Robert

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Question

Find y′ for y = ln(1 − x).

Derivatives

Robert

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Question

Find y′ for y = (x + 3)−3.

Derivatives

Robert

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Question

Find y′ for y = ln(sin x).

Derivatives

Robert

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Question

Find y′ for y = sin(2x).

Derivatives

Robert

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Question

Find y′ for y = sin2 x.

Derivatives

Robert

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Question

Find y′ for y = cos3(2x).

Derivatives

Robert

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Question

Find y′ for y = sin(ex).

Derivatives

Robert

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Question

Find y′ for y = sin(ln x).

Derivatives

Robert

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Question

Find y′ for y = arctg(x2).

Derivatives

Robert

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Question

Find y′ for y = arctg1

x.

Derivatives

Robert

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Question

Find y′ for y = ln(x2 − 1).

Derivatives

Robert

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Question

Find y′ for y = arcsin√

x.

Derivatives

Robert

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Question

Find y′ for y = arctg√

x.

Derivatives

Robert

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Question

Find y′ for y = arctg x2.

Derivatives

Robert

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Question

Find y′ for y = arctg2 x.

Derivatives

Robert

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Question

Find y′ for y = tg 3x.

Derivatives

Robert

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Question

Find y′ for y = tg ln x.

Derivatives

Robert

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Question

Find y′ for y = tg3 x.

Derivatives

Robert

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Answer

y′ =((3x − 1)6)′ = 18(3x − 1)5

Derivatives

Robert

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Answer

y′ =(e−x

)′= −e−x

Derivatives

Robert

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Answer

y′ =(e1−x2

)′= −2xe1−x2

Derivatives

Robert

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Answer

y′ =(e4x−1)′ = 4e4x−1

Derivatives

Robert

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Answer

y′ = (ln(1 − x))′ = − 1

1 − x

Derivatives

Robert

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Answer

y′ =((x + 3)−3)′ = −3(x + 3)−4

Derivatives

Robert

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Answer

y′ = (ln(sin x))′ =cos x

sin x

Derivatives

Robert

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Answer

y′ = (sin(2x))′ = 2 cos(2x)

Derivatives

Robert

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Answer

y′ =(sin2 x

)′= 2 sin x cos x

Derivatives

Robert

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Answer

y′ =(cos3(2x)

)′= −6 cos2(2x) sin(2x)

Derivatives

Robert

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Answer

y′ = (sin(ex))′ = ex cos(ex)

Derivatives

Robert

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Answer

y′ = (sin(ln x))′ =cos(ln x)

x

Derivatives

Robert

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Answer

y′ =(arctg(x2)

)′=

2x

1 + x4

Derivatives

Robert

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Answer

y′ =

(arctg

1

x

)′=

1

1 +( 1

x

)2 ·(− 1

x2

)

Derivatives

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Answer

y′ =(ln(x2 − 1)

)′=

2x

x2 − 1

Derivatives

Robert

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Answer

y′ =(arcsin

√x)′

=1√

1 − x

1

2

1√x

Derivatives

Robert

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Answer

y′ =(arctg

√x)′

=1

1 + x

1

2

1√x

Derivatives

Robert

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Answer

y′ =(arctg x2)′ =

1

1 + x42x

Derivatives

Robert

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Answer

y′ =(arctg2 x

)′= 2

arctg x

1 + x2

Derivatives

Robert

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Answer

y′ = (tg 3x)′ =3

cos2 3x

Derivatives

Robert

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Answer

y′ = (tg ln x)′ =1

x cos2 ln x

Derivatives

Robert

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Answer

y′ =(tg3 x

)′= 3 tg2 x

1

cos2 x