Find the derivative of (x^2+5x+2)^2

Question

johnnydicamillo · Answer

$$f(x) = (x^2+5x+2)^2$$

johnnydicamillo · Answer

I got $$2x^2+12x+9$$ but its wrong

anonymous · Answer

Chain rule. So the very first thing you can perform a derivative operation on is the exponent of 2. So you would do the normal power rule and then leave the inside unchanged. The inner "layers" of your derivative never get changed, chain rule is just successive multiplication of derivatives. So after the first step, you have:

$2(x^{2}+5x +2)$. 

Now inside of the parenthesis we can perform another derivative operation on the $x^{2} + 5x + 2$ portion. So we'll take the derivative of this and multiply it by what we currently have.

The derivative of $x^{2} + 5x + 2 = 2x + 5$

So this result is then multiplied by what we got from the previous step, giving an answer of:

$2(x^{2}+5x+2)(2x+5)$

johnnydicamillo · Answer

do I need to distribute?

anonymous · Answer

Depends on if you're entering this into a program or just turning in homework to a teacher and whatever they want. If you're entering this into a program as an answer, then yes I would distribute.