cari dy/dx jika y=(2x-3)/(x^2+4)^3 menggunakan aturan rantai pada turunan.

y = u(x) / v(x)
y' = { u'(x).v(x) - u(x)/v'(x) }/ { v(x) }^2
y = (2x -3) / (x^2 +4)^3
u(x) = 2x - 3 => u'(x) = 2
v(x) = (x^2 +4)^3 => v'(x) = 3(x^2+4)^2.2x
= 6x ( x^2 + 4)^2
y' = { 2.(x^2+4)^3 - (2x -3){ 6x( x^2 +4)^2 / (x^2+4)^6
= { 2.(x^2 +4)^3- (12x^2-18x)(x^2+4)^2 ) / (x^2 +4)^6
= {(x^2+4)^2 [2(x^2+4)-(12x^2-18x) } /(x^2+4)^6
= { 2x^2+8 -12x^2-18x}/ (x^2+4)^4
= { -10x^2-18x +8} / (x^2+4)^4