Differentiate. Calculus 1/(x^4+x^2+1)?

Question

1/(x^4+x^2+1)
So I used the quotient rule and got this (x^4+x^2+1)-(4x^3+2x)/(x^4+x^2+1)^2 but the answer I get does not match the back of the book. Please help and thank you :)

Answer 1

The expression is 1/(x⁴ + x² + 1).

Differentiate with respect to x.

= (d/dx) [1/(x⁴ + x² + 1)]

= -1/(x⁴ + x² + 1)² * (d/dx)(x⁴ + x² + 1)

= -1/(x⁴ + x² + 1)² * (4x³ + 2x)

= - (4x³ + 2x)/(x⁴ + x² + 1)².

The solution is = - (4x³ + 2x)/(x⁴ + x² + 1)².