# Homework Help: Chain rule

1. Mar 16, 2014

### anthonyk2013

Differentiate the following by rule y=(2x2+4x)5

Is the chain rule the right rule to use?

dy/dx=dy/du*du/dx

Let U=2x2+4x

du/dx=4x+4

y=(u)5 → dy/du=5(u)4

dy/dx=5(u)4*4x+4

dy/dx=5(2x2+4x)4*4x+4

dy/dx= 30(2x2+4x)44x

dy/dx= 30(2x216x)4

I'm wondering if I am on the right track?

2. Mar 16, 2014

### Staff: Mentor

Anthonyk, your questions should be posted in the Homework & Coursework sections (Calculus & Beyond) - not in the technical math sections.

3. Mar 16, 2014

### anthonyk2013

ok no problem

4. Mar 16, 2014

### Ray Vickson

I hope you did not mean what you wrote, which was
$$\frac{dy}{dx} = 5(x^2 + 4x)^4 4x + 4, \text{ which } = 4 +5(x^2 + 4x)^4 4x$$
I hope you meant
$$\frac{dy}{dx} = 5(x^2 + 4x)^4 (4x + 4)$$
If that is what you did mean, that is what you should write; note the parentheses.

5. Mar 16, 2014

### Staff: Mentor

Use parentheses where they are needed.
The right side should be 5u4 * (4x + 4)
That last factor should be (4x + 4)
No. I can't tell what you did here. How did you get 30 at the beginning of the right side?

6. Mar 16, 2014

### vela

Staff Emeritus
In addition to what Ray noted, I can't figure out what you did to get the last two lines. You need to go back and review algebra.

7. Mar 16, 2014

### anthonyk2013

Ya sorry that is what I meant.

can I simplify this further or can I leave it like that?

8. Mar 16, 2014

### Staff: Mentor

You can factor 4 out of the 4x + 4 term, and put it with the 5 factor. Otherwise, that's about all you can do. For most purposes, leaving it in factored form is preferable to multiplying everything out.

9. Mar 16, 2014

### anthonyk2013

dy/dx=20(2x2+4x)*(4x) this what you mean

10. Mar 16, 2014

### Staff: Mentor

No. Like vela said, you need to take some time to review algebra.

Starting from here:
dy/dx=5(2x2+4x)4 * (4x+4), factor 4 out of the last expression in parentheses, and combine that 4 with the leading 5. You did this, but the problem is that 4x + 4 ≠ 4*x. That seems to be what you're doing.

11. Mar 17, 2014

### anthonyk2013

dy/dx=5+4(2x2+4x)44x

dy/dx=9(2x2+4x)44x

or

dy/dx=10x2+20x*(4x+4)

Last edited: Mar 17, 2014
12. Mar 17, 2014

### BruceW

none of those. take your time, just using rules of arithmetic that you are certain about. for example, (4x+4) = 4*(x+1) right? So then what does the equation look like?

13. Mar 17, 2014

### anthonyk2013

I know this is probably very simple I just cant get it.

dy/dx=5(2x2+4x)*(4x+4)

Do I separate it out and treat 5(2x2+4x) from (4x+4)

5(2x2+4x)*4(x+1)?

14. Mar 17, 2014

### BruceW

yeah, almost. you forgot the first bit should be to the power of four. so it is 5(2x2+4x)4*4(x+1) And yes, it is fine to 'separate out'. In arithmetic, it is always OK to say a*(b*c)=a*b*c i.e. in this case 5(2x2+4x)4*(4x+4) = 5(2x2+4x)4*4(x+1)

15. Mar 17, 2014

### anthonyk2013

5(2x2+4x)4*4(x+1)

Thanks very much, frustrating that its so simple. thanks again

16. Mar 17, 2014

### BruceW

glad to have helped! yeah, I'm writing Makefiles at the moment, which should be a simple programming thing to do. But it's taking me ages! haha

17. Mar 17, 2014

### anthonyk2013

Best of luck.

18. Mar 17, 2014

### Staff: Mentor

You are really not going to be able to do calculus unless you have good facility with algebra. You did not realize that you could combine the factors 5 and 4 to give 20. Your previous posts had several algebra errors in them. I implore you to please follow Vela's advice and review algebra.

Chet

19. Mar 17, 2014

### anthonyk2013

Thanks I have been looking over it today. It's just the work load of study, job and kids I can only do so much.

I can multiply 5*4 to get 20. Can I do anything with what in the bracket?

20. Mar 17, 2014

### Staff: Mentor

Yes, you can factor out a 2, and, when it comes out of the bracket, it becomes 24=16, which, when multiplied by the 20 becomes 320.

Chet

21. Mar 17, 2014

### vela

Staff Emeritus
You'll be much more efficient at studying once you get the algebra down. You don't want to be wasting time struggling with algebra instead of concentrating on the material you're supposed to be learning. I'll note that with this problem, you had the calculus part — applying the chain rule — done correctly; it was only the subsequent algebra that was a problem. It might feel like reviewing algebra is a low priority, but you really should make it a higher one.

22. Mar 17, 2014

### Staff: Mentor

I agree with what vela and Chet have said. I recognize that you have a lot of time constraints at the moment, with kids, job, and school, but a small amount of time spent at bolstering your algebra skills (say, 30 minutes of focused effort a day) will save a lot of time down the road.

23. Mar 17, 2014

### anthonyk2013

I will try and put some time aside for algebra, thanks for advice and help I appreciate it. Cheers and happy st Patrick's day :-)