Aditivos
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Correção dos exercícios da apostila1) y = x3. log(x) ( y’ = u’.v+u.v’ = 3x².log(x) +x³.1/x.ln10=3x².log(x) +x²/ln10
2) y = -0,6x ( y’ = -0,6
3) y = x[pic]= x.x1/2 = x3/2 ( y’ = 3/2 .x1/2 = 3/2 [pic]
4) y = 3-x6+x8 ( y’=-6x5+8x5
5) y = -x3 (y’=-3x2
6) y =[pic].x –1= xx1/2x-1 = x-1/2 (y’ = -1/2 x-3/2[pic]
7) y = 4x+5x2+6x3+7x4 (y’=4+10x+18x2+28x3
8) y= 6x2+ 7-x ( y’ = 12x-1
9) y = [pic] ([pic]
10) y =[pic] ( y’ = ¾
11) y = [pic] ( y’ = ½
12) y = [pic]([pic]
13) y = [pic] ( y’ = [pic]
14) y =[pic] (y’= [pic] =[pic]
15) y = [pic] ( y’ = [pic]
16) y = [pic]=(x²-5x)1/3 ( y’ = 1/3 (x²-5x)-2/3.(2x-5) = [pic]
17) y = [pic] ( y’= [pic]
18) y = x2.(2x-1)4 ( y’ = 2x(2x-1)4+x².4(2x-1)³.2=2x(2x-1)4+8x²(2x-1)³
19) y = [pic] (y’=[pic]
20) y = [pic] ( y’ = 4.(-5/2)x-7/2 = [pic]
21) y = [pic] ([pic]
22) y = 7.ex + ln(x) - ln 2 (y’=7ex+1/x
23) y = 6x 0,5 ( y’ = 3x-0,5
24) y = 0,2x+0,5x2-0,3 ( y’=0,2+x
25) y = [pic]-3x+5= x1/5-3x+5 (y’=[pic]-3
26) y = [pic]=x1/5+x1/3 (y’=[pic]=[pic]
27) y = [pic]=(3x+9)1/2 ( y’ = ½ (3x+9)-1/2 .3 = [pic]
28) y = 10x + 5. ln(x) + 3x+4 ( y’=10x.ln10+5.1/x+3
29) y = 5. ex+ 6. ln(x) +3. 2x + 6 (y’=5.ex + 6.[pic]+3.2x.ln2
30) y = (ln(x))3 ( y’ = 3.(ln(x))².1/x = [pic]
31) y =5.3x ( y’ = 5.3x.ln3
32) y = 12x + x3 ( y’=12x.ln12+3x2
33) y = x2.ex ( y’ = u’.v+u.v’ = 2x.ex+x².ex
34) y = (3x2+5)5 ( y’ = 5.(3x²+5)4.6x =30x(3x²+5)4
35) y = (2x-4)3 ( y’ = 3.(2x-4)³.2=6(2x-4)³
36) y = -x.ln(x) ( y’ = u’.v+u.v’ = -1.ln(x) +(-x).1/x = -ln(x) -1
37) y = (x3 –3x2)4 ( y’ = 4(x³-3x²)3(3x²-6x)=(x³-3x²)³ (12x²-24x)
38) y = (4 – 7x)7 ( y’ = 7.(4-7x)6.(-7) = -49(4-7x)6
39) y = (e5x+3)4=e20x+12 (y’ = 20e20x+12
40) y = [pic] ( y’ = 2x[pic]
41) y = 2.e3x-1 ( y’ = 2.3 e3x-1 = 6.e3x-1
42) y = 5x – 3x2 +4 (y’=5-6x
43) y = e5-2x (y’ = -2.e5-2x
44) y = 5.e2-x ( y’ = 5.(-1) e2-x = -5 e2-x
45) y =2x. x2 (y’ = u’.v+u.v’=2x.ln2.x²+2x.2x