pochodne

Zadania + Rozwiązania

Oblicz pochodną funkcji:

» /(x) = 5x

>    f(x) = 3x⁷

>    f(x) = a:⁵ + x² + 4

» /(x) = 3sfx

» f(x) = £

» f(x) = x⁴ » /(x) = 5x - 3

>    /(x) = 6x⁴ - 3x² + 5x

>    f(x) = sfa?

>    f(x) = £ + v/i

Oblicz pochodną funkcji:

» /(*) = ttś > /(^x) = ISf » /(*) =

Oblicz pochodną funkcji:

>    /(x) = §x⁴ - %x⁶ + l|x + §x⁵ + 10

>    f(x) = ax⁷ - | + c

» f(x) = 8x⁴ - 2x^-3 + 5x¹³ » f(x) =

» f(x) = 5 z[x - 3x² + | \/x®

^y = ih-y*

3> y = 3x° -fx

» y = (3x² — 2\Jx)(2x⁴ — Sś/ic⁴)

»»= 3^2

V ⁼ \Ox'-:ix-+7

»y = 7^r#

^^y- 2+1

>    /(x) = (5x + 4)⁸

» /(^x) = (e - ^5x2)⁷

>    /(x) = \/x² + 5 » /(^x) = 73^+f

>    f (x) = 10x²³ + 5x¹² + ^x² » /(*) =

» /(x) = 3x3 _ 10x3^ + 4x3 + 10*

>    f(x) = 3v^

» f (x) = y/x - f \/x2 - 5\/x³

^ y⁼    + 3xh ~ *75

*y =

» t/ = (—3x² + ^ + 10)(^x — 5x) ^ V ⁼ 373+77+7 y ~ -3i⁵-6i¹+8i

» y = -^4xg²Ą³1^x+2

V ⁼ (I-I³)(2+5x-^)

>    y =

» /(x) = (6x² — 3x + 2)⁵ » /(x) = (5x³ - Jj- + 10)”

»/(^x) = lyPW

^{>    =} ^P+7

» /(x) = ^

5+x2 » /(x) = 2sinx

»/(^x) = iń

» f(x) = sin f

>    f(x) = 10 sin § f(x) = sin² 3x

» f(x) = . ²

>    /(*) = "sc^sT » /(^x) = Tifrf

/(x) = sin x — 5 cos⁴ x

>    y = tg⁵ yx

» /(x) = 10e^x » /(a:) = e^x sinx — 2e^x » /(x) = e⁵x(3sinx - cosx)

>    f(^x) = ^sin2 \fl

»/(^x) = Ś£f-3^7

2> /(i) = \Jcosx - \Jx + 3^/0?

»/(*) = ²ft*$5=

jg> /(x) = (3 sin⁴ x — 2 sin x) cos x » /(x) = e^4x

>    /(x) = xe^x » /(x) = e^cosx »/(x) =e“^in2x

3> /(*) = (a:³ — 5x² + 7x — l)e^x » /(x) = <*³3-^^e-» /(x) = 8^X + 3^X » f(x) = 5 • 8^X + 5 » /(x) = 3^X ■ 7^2x » /(x) = 12 ln x » f (x) = ln 5x » /(x) = 4 ln 9x >/(x) = 81n^

»/(x) = 5 ln _x_j_xi__l

»B = ln(|±|i|f|

» /(x) = ln (sin §x)² » f(^x) = ⁸ ln tg h + ^S,n2x-3^X

» /(x) = ln(ln(lnx))

» /(x) = lncosx

»y = ln(l + §)

y = log_t ln x » f (x) = x^3x

>    /(x) = x^sinx

»/(*) = (!)“

» /(x) = 6^lnx

» /(x) = x^

» f(x) = (ctg x)^cos x » /(x) = (sinx)^tgx

» f(^x) = x^eX »/(*) = (1 + i)¹

3> /(x) = arcsin4x 2> /(i) = arc tg (2x³ - x)

/(x) = arc sin Vx®

3> /(x) = arc sin \/x² — 1 + arc cos y/x'² — 1

»	2 = '	s/ax^2 + bx + c
>	m	1 V5x-4x^J
>	/(*)	1 ■</{<•*+Ł)^Ł
>	/(*)	/x^3-2x^2+3 Y^f+573+7
>	m	_ 4/3-v/t V 3+v7
>	f(^x)	= X COS X
>	/(*)	= sin x cos x — ctg x
>	/(*)	= 5 cos 3x
>	/(*)	= 5x^2 + cos 5x
>	f(^x)	c 4 1 = —5cos qX
>	fi^x)	10 cos^4 5x
>	f(^x)	= ęosx , _3^ 2x 3- cosx
>	/(*)	cosx+sin x
»	y = :	i- sin^2 x — | sin^3 x + | sin^5 x
>	y = *	i ctg^2 x + ctg^4 x
>	/(^x)	= x^2e^x
>	/(*)	e*+s^3 4e^J
>	/(*)	= x^3e^4x cos x
>	/(*)	= 5 cos^4 3x^2
>	/(*)	7 COS^3 X sin^5 x
>	/(*)	= yj2 + tg (x — J)
>	/(*)	= tg x + ctg x + 3x
>	/(*)	= (sinx + cosx)(tgx + ctg
>	/(*)	= 2e3^x
>	/(*)	= 5x^2e^_3x
>	/(*)	= 6e^sinx
>	/(^x)	_ Ąe2 cos^4 x
>	/(*)	= (7x^3 — 2x + l)e^x2_1
>	/(*)	= (x + 2v'6-x^2)e^3x“^1
>	/(*)	= 5^xx^4
»	/(*)	= 5 ■ 10^4x
»	/(*)	= 2^5x3^6xx^9
>	/(*)	= 7 + log2 x
»	f(^x)	^= l°g3 8^77
>	f(^x)	= log5 {x-y/3- X^2)
»	f(^x)	= l°g4 v/fS
>	f(^x)	= log2(log3x)
>	f(^x)	= log7tg(|7T+ix)
>	f(^x)	l°g3 \j l+cosx
>	f(^x)	= sin(log5(x^2 — 2x))
>	f(^x)	^losł^rf
>	f(^x)	~ *°^gv/3
>	y = l	og (e^3x + e-^2x)
>	y = 1	ogx 54

: 8x^_7x : 4x^COSX

i

X*

. ^ln 2x

>    / (x) = arc tg \/x² + 1 - x 3> /(x) = arc sin v^l — x² — 1^

3> /(x) = arc sin » /(x) = arc tg

>    /(*) = arc cqst

» /(x) = x² arc tg x⁴ » f (x) = 3 arc tg(2 tg x + 1)

» /(a;) > /(*) » /(a:) » /(*)

>    /(a:) » /(a:) » /(^x)

>    /(*) » /(a;) » /(a:)

>    f(x)

>    /(*) » /(*) > /(*) » /(a:)

» /(a:) » /(a:) » fi^x) » /(*) » /(a;)

: (cOSx)^SinX

: (t.gx)^

: e^c'

■■ X^x*

9 arc cos ^x

= arc ctg V*² —1

: arccos2x\/l — x² : (2x + 1) arc ctg x ^: |x⁵ arc cos x — |(x⁴ + x³)

= arc cos

arc ctg fj-J:

-    »rcclg3r

1—5x

_    1 3 arc cc

-    75 3+2 ar,