# Thread: Compostion and chain rule

1. ## Compostion and chain rule

How do i do (x^2+2x+7)^4 and find F'(x)

2. ## Re: Compostion and chain rule

Originally Posted by gbaby91
How do i do (x^2+2x+7)^4 and find F'(x)
I would need to apply this rule for your function:$\displaystyle \frac {df}{dx} = \frac {df}{dg} \, \frac {dg}{dx}$

which is of the type f ∘ g (x) ≡ f [g (x)], can you tell why?

What have you tried so far?

dokrbb

3. ## Re: Compostion and chain rule

first i just tried to take the derivative but then i forgot about it being up to the fourth power

4. ## Re: Compostion and chain rule

So, you get f(x)= (x^2+2x+7)^4

5. ## Re: Compostion and chain rule

see at first i didnt think that was correct to bring the 4 out to the front

6. ## Re: Compostion and chain rule

Hmmm...

Well, when you're using the Chain Rule, you take the exponent of the polynomial, multiply it by the whole expression and subtract the exponent by one, and you multiply all of that by the derivative of the original expression without the exponent.

So the first step would look like this:

4 (x2 + 2x + 7)3 d/dx (x2 + 2x + 7)

Now you can find the derivative of x2 + 2x + 7

Hope that helps

7. ## Re: Compostion and chain rule

i guess i just need a step by step help with this answer because i really am confused and i cant remember how to do it

8. ## Re: Compostion and chain rule

Originally Posted by gbaby91
i guess i just need a step by step help with this answer because i really am confused and i cant remember how to do it
you need to figure out "which function is contained in which" if I can express myself in this way:

for example, f' of f(g(x)) = f'(g(x))*g'(x),

in your case (2x^2 + x)^3 = ((2x^2 + x)^3)'*(2x^2 + x)'

is it clear now,

dokrbb

9. ## Re: Compostion and chain rule

Originally Posted by gbaby91
i guess i just need a step by step help with this answer because i really am confused and i cant remember how to do it

$\displaystyle \\y=(x^2+2x+7)^4\\y'=4(x^2+2x+7)^3[2x+2]\\y'=8(x+1)(x^2+2x+7)^3$

10. ## Re: Compostion and chain rule

Thank you Plato i understand now exactly what i was doing wrong and i understand how to do other problems like this