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Temario:
1) y= -5 0 64 7 9.
y= 5/2 9 0 7 Ninguna de las anteriores.
3) y= 250 8 0 7 9/8.
y=16/8 7 66 0 7/6.
5) y= c 8/5 0 7 Ninguna de las anteriores.
1) y= sec 4x dy/dx=4 csc x∙tg 8x dy/dx=4 sec 4x∙tg 4x dy/dx=4 sec 7x∙tg x 0.
2) y= sec x dy/dx=sec x∙tg x dy/dx=sen x∙tg x dy/dx=sec x∙tg 2x dy/dx=sec 8x∙tg 7x.
y= sec 2x² dy/dx=4x Cos 2x² 2 ∙tg 2x² 2 dy/dx=4x Tg 2x² 2 ∙tg 2x² 2 dy/dx=4x sec 2x² 2 ∙tg 2x² 2 dy/dx=4x sec 8x² 2 ∙tg 2x² 2.
y= sec 3x² 5 dy/dx=15x² (4 ) sec 1x² 5 ∙tg 6x² 5 dy/dx=15x² (4 ) sec 3x² 5 ∙tg 3x² 5 dy/dx=15x² (4 ) Csc 3x² 5 ∙tg 7x² 5 dy/dx=15x² (4 ) sec 3x² 5 ∙Sen 3x² 5.
5) y= sec 16x dy/dx=6 sec 2x∙tg16x dy/dx=16 sec16x∙tg16x dy/dx=16 cos 16x∙tg16 dy/dx=16 Csc 16x∙tg16x.
y= arc sec 1/x dy/dx=1/√(1-x 2 ) dy/dx=1/√(1-x² 2 ) dy/dx=1/√(1-x² 2 ) dy/dx=1/√(1-x² 2 ).
y= Lu x³3 dy/dx=3x²/x³ dy/dx=3x²/x³ 3 dy/dx=3x8/x³ 3 dy/dx=1x²/x³ 3 .
2) y= Lu 2x dy/dx=2/2x dy/dx=5/3x dy/dx=5/2x Ninguna de las anteriores .
y= Lu 2x² dy/dx=4x/3x dy/dx=4x/2x dy/dx=4x/2x² dy/dx=8x/2x² .
y= Lu √b-ax dy/dx=-a/4√b-ax dy/dx=-a/2√b-ax dy/dx=-a/4√b-ax dy/dx=+a/5√b-ax.
y= 5x sen x dy/dx=x cos x+sen x 5² x sen x Ln 5 dy/dx=x cos x+sen x 4² x cos x Ln 50 dy/dx=x cos x+sen x 7² x sen x Ln 7 dy/dx=x cos x+sen x 8² x sen x Ln 6.
y= 3²2x dy/dx= 4²x Ln3 2 dy/dx= 3²x Ln3 2 dy/dx= 3²x Ln3 1 Ninguna de las anteriores.
1.F(x)=arc tg u Sol. F(x)=a/(1+u² 2 ) Sol. F(x)=u/(1+u² 2 ) Sol. F(x)=u/(1+u² 5 ) Sol. F(x)=u/(sen+u² 2 ).
F(x)=arc tg 3x² Sol.f(x)=6x/(1+7x²2 ) Sol.f(x)=6x/(1+3x²2 ) Sol.f(x)=6x/(1+9x²2 ) cos(x)=6x/(1+9x²2 ).
F(x)=arc tg √x Sol. F(x)=1/(1+x) 1/2√x=1/(2√x1+x Sol. F(x)=1/(1+x) 1√x=1/2√x0+x Sol. F(x)=1/(1+x) 8/3√x=1/2√x9+x Sol. F(x)=1/(1+x) 2√x=1/2√x1+x.
Ctg2x 2 - csc²2x 2 - csc²x 2 - Sen³2x 2 - csc²5x.
Ctg5x² x – csc² 5x² 10x – csc² 5x² 10x – csc² x² 5x – csc² 5.
Ctg2x² x – csc² 2x² 4x – csc² x² 4x – csc² 2x² 4x – csc 5x² .
Ctg6x² 12x – csc² 6x² x – csc² 6x² 12x – csc² 6 0.
6x^5+4x^2 d/dx 30x^4+8x d/dx 10x^4+6x d/dx x^4+8 1.
-3x^4-x^5+3x^5 4 dy/dx 12x³-5x^4+3 dy/dx 2x³-5x^9+1 dy/dx 5x³-5x^4+3.
14x^2+8x^9-133 dy/dx 28x+2x dy/dx 11x+72x^8 dy/dx 28x+72x^8 dy/dx 28x+1x.
8x+4x^-2+9 dy/dx 1-1x^-3 dy/dx 8-8x^-3 dy/dx 7-8x^-5 1.
12x^-3+4x^4-x^4 dy/dx-33x^(-4)+16x^4 dy/dx-36x^(-4)+16x^3 dy/dx-36x^(-5)+16x^3 dy/dx-13x^(-4)+16x.
(4x-5)^2 dy/dx 8(6x-7) dy/dx 8(4x-5) dy/dx 8(5x-2) dy/dx 8(7x-6).
(4x-2)^2 dy/dx 8(4x-2) dy/dx 8(6x-2) dy/dx 8(1x-2) dy/dx 8(4x-2).
(4x^3-2x)^2 dy/dx 2(4x^3-2x)(12x^2-2) dy/dx 2(7x^5-2x)(1x^2-2) dy/dx 2(5x^3-2x)(1x^2-2) 0.
(3x^2-x)^2 dy/dx 2(5x^2-x)(5x-3) dy/dx 2(4x^2-x)(6x-0) dy/dx 2(3x^2-x)(6x-1) dy/dx 2(4x^5-x)(6x-1).
(6x^4-x+3x^2)^3 dy/dx 3(6x^4-x+3x^2)^2(24x^3-1+7x) dy/dx 3(6x^4-x+3x^2)^2(24x^3-1+6x) dy/dx 3(6x^4-x+3x^2)^2(24x^3-1+6x) dy/dx 3(6x^4-x+3x^2)^2(24x^3-1+x).
sec^2 3x-1 dy/dx6sec^2(3x)tan(3x) dy/dx6sec^2(3x)tan(4x) dy/dx6sec^2(3x)tan(8x) dy/dx6sec^2(3x)tan(x).
sec²x dy/dx 2\sec ^2(x)tan (1) dy/dx 2\sec ^2(x)Sen (x) dy/dx 2\sec ^2(x)tan (x) dy/dx 2\sec ^2(x)tan (1/5).
sec^2 4x+2 dy/dxsec ^2(4x)Cos(4x) dy/dxsec ^2(4x)tan(2x) dy/dxsec ^2(4x)Sen(4x) dy/dxsec ^2(4x)tan(4x).
sec² x³-1 dy/dx6x^2sec ^2(x^3)Sen(x^3) dy/dx6x^2sec ^2(x^3)tan(x^3) dy/dx6x^2sec ^2(x^3)tan(1^2) Ninguna.
sec²6x^5-2x+1 dy/dx 6x^2sec ^2(x^3)Sen(x^3) dy/dx 6x^2sec ^2(x^3)tan (x^3) dy/dx 6x^2Cos ^2(x^3)tan (x^3) dy/dx 6x^2Tang ^2(x^3)tan (x^3).
arc cos x dy/dx (-1)/√(1-x² ) dy/dx (-1)/√(7-x² ) dy/dx (+1)/√(8-x² ) dy/dx (-3)/√(5-x² ).
- arc cos2x dy/dx (-2)/√(1-(2x)^2 ) dy/dx (-2)/√(1-(3x)^4 ) dy/dx (-2)/√(1-(7x)^3 ) dy/dx (-2)/√(1-(1x)^1 ).
arc cos √2x dy/dx (2/(2√2x))/√(1-(√1x)^3 ) dy/dx (2/(2√2x))/√(1-(√2x)^2 ) dy/dx (2/(2√4x))/√(1-(√6x)^4 ) dy/dx (2/(2√3x))/√(1-(√4x)^3 ).
arc cos 4x^3-1 dy/dx (-2x^2)/√(1-(4x^3-11)^2 dy/dx (-12x^2)/√(1-(4x^3-1)^2 dy/dx (-3x^2)/√(1-(4x^3-4)^2 dy/dx (-4x^2)/√(1-(4x^3-6)^2.
e^x dy/dx e^x (x) dy/dx e^x (4) dy/dx e^x (1) dy/dx e^x (2).
e^2x-1 dy/dx e^(2x-1) (11) dy/dx e^(2x-0) (7) dy/dx e^(2x-1) (2) dy/dx e^(2x-x) (3).
e^(3x^2-2x+1) dy/dx e^(3x^2-2x+1) (x) dy/dx e^(3x^2-2x+1) (6x-2) dy/dx e^(3x^2-2x+1) (6x-2) dy/dx e^(3^2-2x+1) (x-2).
e^√x dy/dx e^√x dy/dx e^√x 1/2√x dy/dx e^√x 1√x dy/dx e^√x 2/2√x.
e^5x dy/dx e^5x (5) dy/dx e^5x (4) dy/dx e^5x (1) dy/dx e^5x (3).
y= Lu √(b-ax) dy/dx=(-a)/(4√(b-ax) ) dy/dx=(-a)/(2√(b-1x) ) dy/dx=(+a)/(2√(b-x) ) dy/dx=(-a)/(2√(b-ax) ).
y= Lu x^4 dy/dx=(4x^3)/x^4 dy/dx=(4x^3)/x dy/dx=(4x^2)/x^2 dy/dx=(x^3)/x^2.
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