Ejercicio de derivación

CÁLCULO DIFERENCIAL

Derivadas

Mediante las reglas de cálculo para derivadas, determine en:
a)
c)
d)+πx-lnx+3cosx


Desarrollo

(3(x+h)35)(2(x+h)4+3)-(3x3+5)(2x4+3)
■(〖(〖3x〗^3+〖9x〗^2 h+〖9xh〗^2+〖3h〗^3)〗^-5&〖(〖2x〗^4+〖8x〗^3 h+〖12x〗^2 h^2+〖8xh〗^3 〖2h〗^4)〗^ +3-&(〖3x〗^3+5)(〖2x〗^4-3))/h
■((〖9x〗^2+9xh+〖3h〗^2)&(〖8x〗^3 h+〖12x〗^2h^2+〖8xh〗^3+2h4))/h
h((〖9x〗^2+9xh+〖3h〗^2 )(〖8x〗^3+〖12x〗^2 h+〖8xh〗^2+〖2h〗^3))/h

y´= (9x2) (8x3)

Y=(4-3〖(x+h)〗^2)/(2(x+h)+11)-(4-〖3x〗^2)/(2x+11)

h

y= (4-3(x+h)2). (2x+11)-(2(x+h)+11). (4-3x2)(4-3x2)(2(x+h) 11) (2x+11)
h1
Y= ((4-3(x+h)^2 )(2x+11)-(2(x+h)+11)(4-〖3x〗^2))/(h(2(x+h)+11)(2x+11))

Y=(8x+44-6x〖(x+h)〗^2-33〖x+h〗^2-(8(x+h)-6x^2 (x+h)+44-33x^2 ))/(h((2x+2h+11)(2x+11)))
Y= (8x+44-6x^3-12xh-6xh^2-33x^2-66xh-33h^2-(8x+8h-6x^3-6x^2h+44-33x^2))/(h(2(x+h)+11)(2x+11))
Y= (-78xh+6xh^2-33h^2+8h-6x^2 h)/(h((2x+2h+11)(2x+11)))
Y=(h(78x+6xh-33h+8-6x^2))/(h((2x+2h+11)(2x+11)))=(78x+8-6x^2)/((2x+11)(2x+11))=(78x+8-6x^2)/〖(2x+11)〗^2

d) +πx-lnx+3cosx