Las Pruebas De La Libertdad

Derivadas

1) y=36x-123
Y=3 u ⅔
Yʹ=3(⅔)u ⅔-1(6)=18(6x-1)

2) y=1(1-3x)
Y=4(1-3x)
Y=12(1-3)-5
y=12(1-3)

3) Y=x²(3x-1)²
Y=(3x-1)² x² y=(3x-1)² (2x)+(x²){6(3x-12)}
U=(3x-1)² y=2x(3x-1)²†6x²(3x-1)
Du=2(3x-1)² (3-0)=6(3x-1)
V=x²
Du=2x²

4) y=x³1-4x
U=x³y=x³{-2(1-4x)}+(1-4x)1/2(3x²)
Du=3y³ y=-2x³(1-4)1/2+3x²(1-4x)1/2
V(2-4x)1/2 y=-2x³1-4x1/2 +3x21-4x1/21
Du=1/2(1-4x)1/2(-4)=-2(1-4x) y=-2x3+3x²(1-4x)1-4x1/2y=-b±b2-4ac1-4x =-14x3+3x²1-4x

5) Y=(3x-1)(2x+5)(x²+3
6x³+15x y=6x-13x³+13x²-39x-15
-12x-5
6x²-13x-5 y=24x³-39x²+26x-39
x²+3
6x-13x³-5x²
-------------------------------------------------
+18x²-39x-156x-13x³+13x²-39x-15

6) y=x33x+1
u= x² =x²=13x+1⅔+x+1⅓2x
du= 2x =x²(3x+1)⅔+2x(3x+1)⅔1
v=(3x+1)⅓ =x²+2x(3x+1)(3x+1)⅔
dv=⅓(3x+1)⅓-1(3)
=(3x+1)⅔= 1

7) y=x(x-1)3
U=xx-131-(x){3(x-1)²}{(x-13)}² =-b±b2-4ac(x-1)
Du=1 x³-3x2+3x-1-3x(x2-2x+1)x-16=3x²-3x2+3x-1-3x3+6x2-3xx-16
V=(x-1)³ y=-2x3+3x2-1(x-1)
Du=3(x-1)²
=3(x-1)²

8) y=x²+a²x²-a²
U=x²+a²y=x2-a22x-(x2+a2)(2)(x2-a)²
Du=2x y=2x3-2a2x-2x3-2a2x(x2-a2)²=-4a²x(x2-a2)²
V=x²-a²

Dv=2x y=x²+x²x²-2x²=x²+4x²-4=1.7777777
F(1)==-4(2)²(1)1²-(2)²= 16(-3)²=-169=1.7777777

9) y=1-2xx2+x-3
V=1-2x
x2+3-3-2-12x(2x+1)(x2+x-3)2
Du=2
V=x2+x-3-2x2-2x+6-2x-1+4x2+2(x2+x-3)2
Du=2x+1 2x2-2x+6-2x-1+4x2+2(x2+x-3)
2x-2x+5(x2+x-3)2
21-21+5((1)2+1-(3)2=0+51=51=5

10) y=2x+71-2x
U=(2x+7)½y=(1-2x)½½x+7½(1-2x)½²
Du=½(2x+7)½ -1(2) y=(1-2x)½(2x+7)½+(2x+7)½(1-2x)½(1-2x)
=(2x+7)-½ = 1(2x+7)½ y=1-2+(2x+7)(1-2x)(2x+7)½(1-2)½
V=(1-2x)½=-b±b2-4ac(2x+7)½(1-2x)=4x-62x+1-(1-2x)³
∆v=½(1-2x)½-1(2)
=-1(1-2)½(-2)(1-2x)½

11) Y=e₅
Y=e₅x
Y=e₅x
Y=5e

12) y=4x3
y=Dxau=au.lnaDxu
y'=4x3lnDx3=4x3ln43x2
3x2.4x3=16.635523
f'1=3(1)2.413ln4=34ln4=16.635523

13) y=2x12x
Y=2x-2x
Y=2xln2Dx(x)-2-xln2Dx(-x)
Y=2xln²-2xln²(-1)
Y=2xln2+2-xln2
Y=2xln2+ln²2x=1.752867F(1)=2(1)ln+ln²2(1)=1.752867

14) y=4ex-ex
y=4e-x-ex y=-4xex-e=4.189799593
y=4e-xD(-x)-exD(x)
y=yxe-x-e

15) t3.e2t
u=t3 y'=e2t3t2+t22e2t
Du=3t3 y'=3t2.e2t+2t3.e2t
V=e2t...