find differentiation of x2/(x2+1)(x2+4)?

Answer 1

Let u = x^2 and v = (x^2 + 1)(x^2+4)
where u and v are functions of x.

So d/dx(u/v) = (vdu - udv)/v^2

du = 2x
dv = 2x(x^2+4) + (x^2+1)(2x) = 4x^3 +10x

vdu - udv = x^2(4x^3 + 10x) - (x^2+1)(x^2+4)(2x) = -2x^5 + 8x
v^2 = (x^4 + 5x^2 + 4)^2

So d/dx(u/v) = (-2x^5 + 8x)/ (x^4 + 5x^2 + 4)^2.. which is the answer.

Answer 2

find differentiation of x2/(x2+1)(x2+4)?
I assume x^2 is the numerator and (x^2+1)(x^2+4) is the denominator.

dy/dx = [(x^4 + 5x^2 + 4)(2) - X^2(4x^3 +10x)]/(x^4+5x^2+4)^2
= (2x^4+10x^2+8 -4x^5-10x^3)/(x^4+5x^2+4)^2

Answer 3

[(x^4 + 5x^2 + 4)(2) - X^2(4x^3 +10x)]/(x^4+5x^2+4)^2
= (2x^4+10x^2+8 -4x^5-10x^3)/(x^4+5x^2+4)^2