Күрделі функцияның туындысы

2. x(t)= - t=2 v=? a=?

3.x(t)12-3t+ t=3c v=?      

4.v(t) +5 a=? t=1                 

5.v(t) + +t a=? t=?          

6.v(t) - +5t a=? t=?          

7. v(t)= -1 t=5c a=?             

8.x(t)=7- +2 t=1 a=? v=?

9.x(t)=12-2t+ t=3 v=? a=?

10.x(t)= - +3t t=1 v=? a=?

1.F(x)= -3x+5. M(0,5 ) tga=?

2.F(x)= + ,M(1:3) tga=?

3. F(x)= +1, M(1:2) tga=?

4. F(x) -4, M(2:3), tga=?

5.F(x)=x +1. M(1:1) tga=?

6.F(x)= -2x-5, M(3:4) , tg=?

7. F(x)= - +5x-1, M(1:1), tga=?

8. F(x)= -4x, M(0:1), tga=? k=?

9. F(x)= -7x+4, M(1;2) , tga=? k=?

1.F(x)=4x- ; =2

2.F(x)=12x+ ; =-1

3.F(x)= , = -2

4.F(x)=1- ; =1

5.F(x)= +2x; = -3

6. F(x)= , = -1

7. F(x)=x- , =2

8.F(x)= x+ , =1

9.F(x)= 3- + , a= -1

Күрделі функцияның туындысы

y=f(g(x))- курделі функция

y'=f'(g(x))*g'(x)

мысалы:

1) y'=( )'= *(2x+1)'=

y=((6x- )'= 5*(6x- )*(6x-13)'=30(6x-

2)y=((2x+1

3)y =( )′=

4)y=(

5)y =( ′= =

6)y=( ) =

y=f(g(x)) функциясының f және g функцияларын анықта

1.y=(x+                   

2.y=                        

3.y= cos(x+ )            

4.y=2ctg(3x)

5.y=sin5x                   

6.y=( x-    7.y=

8.y=

9.y=

10. y= (1+

1.y=(6x-   

2. y= +     

3.y= +   

4.y=       

5. y=( - +       

6.y=(3 +      

7.y=(5- +   

8.y=( +    

9.y=     

10.y=                                                                                                                                

F(x)= . g(x)=5x. u(x)=

1.F(g(x))

2. F(u(x))

3.g(F(x))

4.g(u(x))

5.F(F(x))

6.u(g(f(x))

7.u(f(g(x))

8.g(u(f(x))

9.u(g(x))

              

                                             

                                                 

                                                        

                                                   

Тригонометриялық функцияның туындылары

(sinx)’=cosx;       (ctgx)’= ;     (cosx)’= -sinx;               (tgx)’=  

1.y′=(3cos5x = –3sinx

2.y′=(2cos2x = –2sin2x =–4sin2x

3.y′=(4sinx =4cosx

4.y′=(2sin2x =2cos2x =4cos2x

5.y′=(2cosx+5sinx =–2sinx+5cosx

6.y′=( =2cosx =–sinxcosx=–sin2x

7.y′=(si =3 =3si

8.y′=(3tgx =

9.y′=(2tg2x =

10.y′=( =– = –

11.y′=( =( +( =5si

12.y′=(sin( =cos( + ) =cos( ) =

1. y=3sinx             

2. y=2cosx     

3. y=3ctgx             

4. y=2tgx               

5. y= –sinx             

6. y= –cosx             

7. y= –2ctgx          

8. y= –3tgx             

9. y= sinx+cosx      

10. y=sinx-cosx      

11. y=cos(x – )

12. y=sin(  – x)                                          

13.y=tg(x+ )          

14.y=ctg( +x)              

15.y=cos(2x+п)           

16.y=sinx(3x+ )          

17.y= x            18.y=cosx(1+sinx)         

19.y= tgx                   

20. y=cos2x. x=

21.y=cosx . x=

22.y= x

23.y= x

24. y=2cos4x+6

25.y=2co 4x 

1.y=sin2x

2.y=cos2x    

3.y=tg2x

4.y=ctg2x   

5.y=2sin3x                    

6.y=3cos2x                   

7.y= -cos4x                     

8.y=3tg3x    

9.y=tg2x+

10.y=2cos5x                   

11.y=sin2x-cos2x

12.y=     

13.y=

14.y=ctgx                        

15.y=3 2x+4.5

16.y=sinx(cosx–1)           

17.y= ctgx                

18.y=2 2x+4

19.y=2tg(2x+ )

20.y=sin3x. = -

21. y=sinx . x=

22.y=5 ( -1)

23.y=2 2x                                                   24.y=co 3x

25.y=si 6x                                                                                                                                                                        

1.y= tgx–4ctgx

2.y=4x–sinx

3.y=6cosx–1.2x

4.y=3cosx–4sinx

5.y=sinx–2x

6.y= +sin2x

7.y=cos4x–

8.y= sin3x–

10.y=2ctg3x–2

11. y= x

12.y= x

13.y=2 x+

14.y=2 2x

15.y=ctg4x                        

16.y= x

17.y=2cos(2x+ )    

18.y=4sin( + )

19.y=2 2x+4

20.y=tgx . =

21.y=sin( +x- )

22.y=tg( + )

23.y= 3x+ +2x

24.y=3cosx+4sinx-

23.y= 5x+

Жуықтап есептеуЖуықтап есептеу

F(x)=F( )+F( )

(1+ =1+n

Мысал:

1) = ≈1+

2)0.99 =(1+(-0.004) =1-16

3)(1.00 =(1+0.00 ≈1+200

4)1.00 =(1+0.002 =1+109

5)sinx +cos (x- ) sin36

36 + + = =

sin( )= = (1+ )=

6)sin     sinx≈sin +cos (x- )

= + = + - = + x= +      =

sin( + )≈sin +cos ( + - )= + = (1+ =

7) =1+

8) = =1+

9) = =2 =2(1+ =2

= =5 =5(1+ =5.075   

1.F(x)= +3x x=1.998

2.F(x)= x=3.03        

3.F(x)2x- x=5.002            

4.F(x)=3 x=7.02        

5.F(x)=        

6.F(x)=2 x=2.007

7.F(x)= x=3.031