Prof. M.Sc. Carlos Alberto Bezerra e Silva

Material de apoio - Exercícios – Derivadas - Respostas

a ) Respostas

( )

^{x = 0}

'

f ^f'

( )

^{x = 3}

( )

3

= 1 x '

f ^f'

( )

^{x = 2x f}

( )

^{x = x6}

( )

¹₂

x x '

f = −

( )

³₄

x x '

f = − ^f'

( )

^{x = 1 f'}

( )

^{x = 100x99 f'}

( )

^{x = −3x−4 g'}

( )

^{x = 12 g'}

( )

^{x = −5}

( )

⁹₂

x x '

g = ^g'

( )

^{x = 3x g'}

( )

^{x = 0 g'}

( )

^{x = 0 g'}

( )

^{x = 9 g'}

( )

^{x = −13x−14}

( )

^{x x}

'

g = 8 ^g'

( )

^{x = − x−6 g'}

( )

^{x = 3xln3 g'}

( )

^{x = 4xln4 g'}

( )

^{x = 100xln100}

( )

^{10 10}

10

1 . ln x

'

g = ^{x g'}

( )

^{x = ex f'}

( )

^{x = 88x10 f'}

( )

^{x = −7x2}

( )

^{x x}

'

f = 1+ 6 ^f'

( )

^{x = 10x + 5x4 f'}

( )

^{x = 3x2 + 2x + 1}

( )

^{x = 2nxn−1}

'

f ^f'

( )

^{x = 8x + cosx f'}

( )

^{x = 3x2 − 6x+ 3}

( )

^{x cosx senx}

'

f = −1+ + ^f'

( )

^{x = a− 4x3 f'}

( )

^{x = 32x3 − 3xln3}

( )

^{x senx ex}

'

f = − − ^f'

( )

^{x = 3x2 − 4xln4 f'}

( )

^{x = 20x3− 9}

( )

^{x ln e cosx}

'

f = 5^x 5+ ^x +

b ) Respostas

( )

2 4

2

' 3 ₃

3 2

+

= + x

x x x

f

( ) ( )

3 3 3

1 1

' 2 ₂

3 2

+ +

+ +

= +

x x

x x x x

f

( )

^{x x}

(

^{x x}

)

f' = (−2 − 1)sen ² + ^f'

( )

^{x = 2xcos}

( )

^x2

( )

^{cot ( )}

' x g x

f = ^f'

( )

^{x = 18x}

(

^{3x2 +1}

)

²

( )

^x

( )

^x

f' = −3sen 3

( )

3 ' ₂2

= + x x x f

( )

^{x e x}

f' = 3 ^{3 f'}

( )

^{x = cos}

( )

^x.esenx

( )

^x

( ) (

^{x x}

)

g' = −sen .coscos ^g'

( )

^{x = −exsen}

( )

^ex

( )

^{x e x}

g' = −5 ^{−5 g'}

( )

^{x = sec}

( )

^{x.etg( )x}

( )

⁸

(

^{2 3}

)

³

' t = t t +

g ^g'

( )

^{x = 3sec}

( ) ( )

^{3x.tg 3x}

( )

^{2 cossec2}

( )

²

' x x x

g = − ^g'

( )

^{x = −2cossec}

( )

^{2x cotg}

( )

^2x

( )

^x

( ) ( ) ( )

^{x tgx tg tgx}

g' = sec² .sec .

( ) ( )

x x

x x x x

e e

e e e x e

g ⁻ ₋ ⁻

+ +

= −

2 ' 2

c ) Respostas

( )

^{x = 15x4 + 4x3+ 9x2 + 8x+ 1}

'

g^'

( )

^{x = x2}

(

^{9x6 + 7x4 + 12x3 + 4x+ 3}

)

g^'

( )

^{x x e}

(

^x

)

g = ^{2 x} 3+

( )

^{x e}

(

^x

)

^senx

'

g = ^x + 1 −

( )

^{x x a}

(

^xlnx

)

'

g = ^{3 x} 4+

( )

^{x = acosx− bsenx}

(

^{a,b∈ ℜ}

)

'

g^'

( )

^{x e}

(

^{cosx xcosx xsenx}

)

g = ^x + −

( )

^{x x ex}

'

g = 2 + 2

( )

^{x e .}

(

^{senx.cosx cos x}

)

'

g = ^x + 2

( )

^{x xe}

(

^x

)

'

g = 5 ^x 2+

Prof. M.Sc. Carlos Alberto Bezerra e Silva

Material de apoio - Exercícios – Derivadas - Respostas

( )

¹⁴₈

x x '

f = −

( )

^{x =}

(

^{x2−+2xx−+11}

)

²

' f

( )

^{x =}

(

^x−−21

)

²

' f

( )

^{x =}

(

^{3x23+ 2}

)

²

' f

( ) ( )

²

2

9 2

70 12 27

x x x x

'

f −

+ +

= −

( ) (

³

)

²

2

1 6

= + x x x ' f

( ) (

^{2 3}

)

²

2

1

3 2 1

x x x

x x x

'

f + + +

−

−

= −

( )

^{2 2}₃

x x x '

f = −

( )

7

2 6 +

= x

x ' f

( ) ( )

²

2

1

3 2

x x x x

'

f +

−

= +

d ) Respostas

( )

^{2.3 ln3 3}

' x = ^2x + g

( )

2 1

2 2

' ²

+ +

−

= ⁻

xe x x

g ^x

( )

^{x e x e x}

g' = − ⁻ + 2 ⁻²

( )

^{2 .2 .ln2 2.3 .ln3}

' x x ^{x2 2x}

g = +

( )

^{x x}

(

^x

) (

^x

)

g' = −sen .3+ cos ^x.ln3+ cos

( ) (

^{10 10}

)

^ln10

' x ^{x x}

f = + ⁻

( ) [

^sen

( )

^{6 sen}

( )

^{4 sen}

( )

^{2 1}

]

4

' x = 1 x + x + x +

f

( )

^x

( )

^{x e x ex}

( )

^ex

f' = − sen . ^cos − sen

( )

^{x e}

(

^x

)

f' = ^3x 1+ 3

( )

^{x x e}

(

^x

)

f' = 3 ^{2 −3x} 1−

( ) ( )

1 2 1 2 2 ln

' = + + +

x x x

x f

( )

^{x e}

( ( )

^x

( )

^x

)

f' = ^x cos 2 − 2sen 2

( ) (

²

) (

³

) (

^{14 36}

)

' x = x+ ⁷ x+ ⁵ x+ f

( ) ( )

4 4

1

' 21 ⁴

3

+

= +

x x x x

f

( )

x

x x f' = 2

( ) ( ) ( ) ( )

4

sen cos

sen

' 3 ² x ² x ⁴ x

x

f = −

( )

^x

[ ( )

^x

( )

^x

]

f cos² sen²

8

' = 3 −

( )

^{x x}

f' = sen⁴

( )

^x

( )

^x

( )

^x

f' = −2sen + 2sen³

( )

^{x x}

f' = sen⁵

Prof. M.Sc. Carlos Alberto Bezerra e Silva