# y = (x^2+2)^2(x^4+4)^4 #
Taking Natural Logarithms:
# ln y = ln {(x^2+2)^2(x^4+4)^4} #
# :. ln y = ln (x^2+2)^2 + ln (x^4+4)^4 #
# :. ln y = 2ln (x^2+2) + 4ln (x^4+4) #
Differentiating we get:
# 1/ydy/dx = 2 (2x)/(x^2+2) + 4 (4x^3)/(x^4+4) #
Simplifying;
# 1/ydy/dx = (4x) { 1/(x^2+2) + (4x^2)/(x^4+4) } #
# :. 1/ydy/dx = (4x) { ( (x^4+4) + 4x^2(x^2+2) )/( (x^2+2)(x^4+4) ) } #
# :. 1/ydy/dx = (4x) { ( x^4+4 + 4x^4 + 8x^2 )/( (x^2+2)(x^4+4) ) } #
# :. 1/ydy/dx = (4x) { ( 5x^4 + 8x^2 + 4 )/( (x^2+2)(x^4+4) ) } #
# :. dy/dx = (4x) { ( 5x^4 + 8x^2 + 4 )/( (x^2+2)(x^4+4) ) } y#
# :. dy/dx = (4x) { ( 5x^4 + 8x^2 + 4 )/( (x^2+2)(x^4+4) ) } (x^2+2)^2(x^4+4)^4#
# :. dy/dx = (4x) ( 5x^4 + 8x^2 + 4 ) (x^2+2)(x^4+4)^3#
