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31.- f(x)=(〖(x〗^2+1^ )(2x+3))/(3x-1)

f^' (x)=(〖2x〗^3+〖3x〗^2+2x+3)/(3x-1)

f^' (x)=(3x-1(〖6x〗^2+6x+2)-〖2x〗^3+〖3x〗^2+2x+3(3))/〖(3x-1)〗^2

f^'(x)=(〖18x〗^2+〖18x〗^2+6x-〖6x〗^2-6x-2-〖6x〗^3-〖9x〗^2-6x-9)/〖(3x-1)〗^2
f^' (x)=(〖21x〗^2-6x-6x^3-11)/〖(3x-1)〗^2

32.- g(t)=((t+3)(〖3t〗^2+5))/(2-3t)

g(t)=(3t^3+5t+9t^2+15)/(2-3t)

g^' (t)=(2-3t(9t^2+5+18)-3t^3+5t+9t^2+15(-3))/〖(2-3t)〗^2

g^'(t)=(18t^2+10+36-〖27t〗^3-15t-54t+〖9t〗^3+15t+〖27t〗^2+45)/〖(2-3t)〗^2

g^' (t)=(45t^2-18t^3-54t+91)/〖(2-3t)〗^2

33.- y=(〖(2u〗^3+7) 〖(3u〗^2-5))/(u^2+1)

y=(〖6u〗^5-10u^3+〖21u〗^2-35)/(u^2+1)

y^'=(u^2+1(〖30u〗^4-30u^2+42u)-〖6u〗^5-10u^3+〖21u〗^2-35(2u))/〖〖(u〗^2+1)〗^2
y^'= (〖30u〗^6-〖30u〗^4+42u^3-〖12u〗^6-〖20u〗^4+〖42u〗^3-70u)/〖〖(u〗^2+1)〗^2

y^'= (〖18u〗^6-50u^4-70u)/〖〖(u〗^2+1)〗^2

34.-y=((t+1)(t^2+7t))/(3t+4)
y=((t^3+〖7t〗^2+t^2+7t))/(3t+4)

y^'=(3t+4(3t^2+14t+2t+7)-(t^3+〖7t〗^2+t^2+7t)(3))/〖(3t+4)〗^2
y^'=(9t^3+42t^2+〖6t〗^2+21t+〖12t〗^2+56t+8t+28-〖3t〗^3-〖21t〗^2-〖3t〗^2-21t)/〖(3t+4)〗^2y^'=(6t^3+36t^2+64t+28)/〖(3t+4)〗^2

(35-38) DETERMINE LA ECUACIÓN DE LA RECTA TANGENTE A LAS GRAFICAS DE LAS FUNCIONES SUGUIENTES EN EL PUNTO QUE SE INDICA.

35.- y=(〖3x〗^2+7)(x+2) en(-1;10)

y^'=(〖3x〗^2+7)(1)+(x+2)(6x)

y^'= 〖3x〗^2+7+〖6x〗^2+12x
y^'=〖9x〗^2+12x+7
y=9(-1)^2+12(-1)+7
y(-1)=4

y-y1=m(x-x1)
y-10=4(x+1)
y=4x+4+10
Y=4x+14

36.- y=(x+1)(x^2-1)en x= 1
y^'=x+1(2x)-(x^2-1)(1)

y^'=〖2x〗^2+2x-x^2+1

y(1)=2(1^2 )+2(1)-1^2+1

y(1)=4

37.- y=(2x-3)/(x-2)en (3,3)

y^'=(x-2(2)-2x-3(1))/(x-2)

y^'=(2x-4-2x-3)/(x-2)
y (3)= (2(3)-4-2(3)-3)/(3-2)

y (3)= (6-4-6-3)/1

y(3)= -7

y-y1=m(x-x1)
y-3=-7(x+3)
y=-7x-21+3
Y=7x-1838.- f(x)= (x^2-4)/(x^2+1) en x= -2

f^' (x)=(x^2+1(2x)-x^2-4(2x))/〖(x^2+1)〗^2

f^' (x)= (〖2x〗^3+2x-〖2x〗^3+8x)/〖(x^2+1)〗^2

f^'...
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