TALLER DE EJERCICIOS 2 (REGLAS DE DERIVACIÓN, INTEGRAL INDEFINIDA, METODOS DE INTEGRACIÓN).

TALLER DE EJERCICIOS 2 (REGLAS DE DERIVACIÓN, INTEGRAL INDEFINIDA, METODOS DE INTEGRACIÓN)

Derive las siguientes expresiones

1.x^5 f^' (x^5)=5x^(5-1)=5x^4

2.x^√3 f'( x^√3)=√3 x^(√3-1)=√3 x^(0,7)

3.1/( t^3 ) f^' (t^(-3) )=-3x^(-3-1)=-3x^(-4)=-3/x^4

4.4/( u^4 ) f^' (4u^(-4) )=4(-4)u^(-4-1)=-16u^(-5)=-16/u^5

5.1/( 〖5u〗^5 ) f^' (1/5 u^(-5) )=1/5(-5)u^(-5-1)=-u^(-6)=-1/u^6

6.x^7/( 7^ ) f^' (x^7/( 7^ ))=1/7 〖(7)x〗^(7-1)=x^6

7.1/( ∛(x^2 ) ) f^' (x^((-2)/3) )=(-2)/3 x^((-2-3)/3)=〖(-2)/3 x^((-5)/3)= 〗^ -2/(3√(3&x^5 ))

8.2x-x^3= f^' (2x)- f^' (x^3 )=2-3x^(3-1)=2-3x^2

9.4x^3-3x^2+7= f^' (4x^3 )- f^' (3x^2 )+ f^' (7) =3(4) x^(3-1)-3(2) x^(2-1)+0 =12x^2-6x

10.5-2x^2+x^4= f^' (5)- f^' (2x^2 )+ f^' (x^4 ) =0-2(2) x^(2-1)+4x^(4-1)

=4x^3-4x

11.3x^4-7x^3+5x^2+8 = f^' (3x^4 )- f^' (7x^3 )+ f^' (5x^2 )+ f^' (8) =3(4) x^(4-1)-7(3) x^(3-1)+5(2) x^(2-1)+0

=12x^3-21x^2+10x

12.4x^3+2+ 1/x = f^' (4x^3 )- f^' (2)+ f^' ( x^(-1) ) =4(3) x^(3-1)-0+(-1) x^(-1-1)

=12x^2-1/x^2

13.3u^2+ 3/u^2 = f^' (3u^2 )+ f^' ( 〖3u〗^(-2) ) =3(2) u^(2-1)+3(-2) u^(-2-1)

=6u^ -6/u^3

14.x^6/6+ 6/x^6 = f^' (x^6/6)+ f^' ( 〖6x〗^(-6) ) =1/6 (6) u^(6-1)+6(-6) x^(-6-1)

=〖u^ 〗^5-36/x^7

15.x^1,2+ 1/x^0.6 = f^' (x^1,2 )+ f^' (x^(-0,6) ) =1,2x^(1,2-1)+(-0,6) x^(-0,6-1)

=1,2 x^(0,2)-(0,6)/x^(1,6)

16.x^0,4- 1/x^0.4 = f^' (x^0,4 )- f^' (x^(-0,4) ) =0,4x^(0,4-1)-(-0,4) x^(-0,4-1)

=(0,4 )/x^(0,6) +(0,4)/x^(1,4)

17.2√x+ 2/√x= f^' (2√x)+ f^' (2/√x ) =2(1/2) x^((1-2)/2)+2(-1/2) x^((-1-2)/2)

=x^(-1/2)-x^(-3/2)= 1/√x-1/√(x^3 )

18.x^7+ 1/x^7 +7x+7/x+7= f^' (x^7 )+f^' (x^(-7) )+ f^' (7x )+f^' (7x^(-1) )+ f^' (7

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