Derivative of $f(x) = (x^2 +1)^3 (2x+5)^2$ I have function
$$f(x) = (x^2 +1)^3 (2x+5)^2$$
I need to find the derivative.
I believe that I need to use the product rule and chain rule.
Here's what I did.
$$f'(x) = (2x+5)^2[3(x^2+1)^2(2x)] + (x^2+1)^3[2(2x+5)2]
\\ = (2x+5)^2(6x(x^2+1)^2)+4(2x+5)(x^2+1)^3
\\ = 6x(2x+5)^2(x^2+1)^2+4(2x+5)(x^2+1)^3$$ 
That is what I have.
But the problem is, the answer book says that the answer is,
$$2(x^2+1)^2(2x+5)(8x^2+15x+2)$$
Since the answer book has been wrong few times, so I checked the answer with a calculator.
The calculator showed the same answer.
Then I used another calculator (which showed some steps), showed my answer.
The calculator showed, 
Which answer is correct?? Or are they just equivalent answers??
If I did wrong, what was the problem??
Can it be factorized? How?
Thank you

Factor out common terms:
$6x(2x+5)^2(x^2+1)^2+4(2x+5)(x^2+1)^3=2(2x+5)(x^2+1)^2[3x(2x+5)+2(x^2+1)]=$
$$2(2x+5)(x^2+1)^2[6x^2+15x+2x^2+2]=$$
$$2(2x+5)(x^2+1)^2(8x^2+15x+2)$$
both the textbook and you are correct.
