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# C3 The Product Rule Question watch

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

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