aligned & If d d x ( x^2+1 (x^2+5 ) (x^2+9 ) ) & = 2 x (x^2+1 ) (x^2+5 ) (x^2+9 ) [ 1 f(x) - 1 g(x) - 1 h(x) ] & then 2 h(x)-f(x)-g(x)= aligned

Step-by-step solution

aligned & y= x^2+1 (x^2+5 ) (x^2+9 ) & y= (x^2+1 )- (x^2+5 )- (x^2+9 ) & 1 y d y d x =2 x [ 1 x^2+1 - 1 x^2+5 - 1 x^2+9 ] & d y d x = 2 x (x^2+1 ) (x^2+5 ) (x^2+9 ) [ 1 x^2+1 - 1 x^2+5 - 1 x^2+9 ] & f(x)=x^2+1, g(x)=x^2+5, h(x)=x^2+9 & 2 h(x)-g(x)-f(x)=12 aligned