You are Here: Home >< Maths

# C3 The Product Rule Question

Announcements Posted on
Four hours left to win £100 of Amazon vouchers!! Don't miss out! Take our short survey to enter 24-10-2016
1. Hi,

I was doing a question from C3 about the product rule but I didn't get the right answer and don't understand where I went wrong, my workings are below:

Find dy/dx of sqrtx(5x-4)^3
u = sqrtx differentiating this gave me 1/2x^-1/2
v = (5x-4)^2
a = 5x-4 so differentiating this got me 5
b = a^3 so differentiating this got me 3(5x-4)^2
dv/dx therefore = 15(5x-4)^2
dy/dx = 15sqrtx(5x-4)^2 + 1/2x^-1/2(5x-4)^3
= 15sqrtx(5x-4)^2 + (5x-4)^3/2sqrtx
=2sqrtx15sqrtx(5x-4)^2 + (5x-4)^3 / 2sqrtx
=30x(25x^2-40x+16) + (5x-4)^3 / 2sqrtx
=875x^3-1500x^2+720x-64 / 2sqrtx

Thanks in advance if you can help at all/point out where I've gone wrong

Blake
2. Reading through your solution I see nothing wrong; maybe it's just a case of getting the answer in the form required?
3. (Original post by Blake Jones)
Hi,

I was doing a question from C3 about the product rule but I didn't get the right answer and don't understand where I went wrong, my workings are below:

Find dy/dx of sqrtx(5x-4)^3
u = sqrtx differentiating this gave me 1/2x^-1/2
v = (5x-4)^2
a = 5x-4 so differentiating this got me 5
b = a^3 so differentiating this got me 3(5x-4)^2
dv/dx therefore = 15(5x-4)^2
dy/dx = 15sqrtx(5x-4)^2 + 1/2x^-1/2(5x-4)^3
= 15sqrtx(5x-4)^2 + (5x-4)^3/2sqrtx
=2sqrtx15sqrtx(5x-4)^2 + (5x-4)^3 / 2sqrtx
=30x(25x^2-40x+16) + (5x-4)^3 / 2sqrtx
=875x^3-1500x^2+720x-64 / 2sqrtx

Thanks in advance if you can help at all/point out where I've gone wrong

Blake

You go the right answer at and past that point I don't understand why you're expanding. Just factor out a common term and leave it at that.
4. (Original post by RDKGames)

You go the right answer at and past that point I don't understand why you're expanding. Just factor out a common term and leave it at that.
Why didn't I see that? XD Thanks

## Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank
2. this can't be left blank
3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty
1. Oops, you need to agree to our Ts&Cs to register

Updated: August 12, 2016
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Today on TSR

### Who is getting a uni offer this half term?

Find out which unis are hot off the mark here

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read here first

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams