# Math Help - How do you derive...

1. ## How do you derive this...?

HEY!
I'm new here and I was wondering how to derive something like:

I can do the chain and product rule however the 3 has confused me...

Any working would be appreciated

Challenge accepted?

2. ## Re: How do you derive...

Hey asdfpjdfj.

d/dx (a*f(x)) = a*d/dx(f(x)).

3. ## Re: How do you derive...

Yes, your function, $f(x)=\frac{8(10-x)^2\cdot\sqrt{5(x-5)}}{3}$ can be written $f(x)=\frac{1}{3}\left(8(10-x)^2\cdot\sqrt{5(x-5)}\right)$, so you use chiro's suggestion with $a=\frac{1}{3}$.

- Hollywood

4. ## Re: How do you derive this...?

Originally Posted by asdfpjdfj
HEY!

Any working would be appreciated
Challenge accepted?
I suggest writing it as:
$\frac{1}{3}\left(8(10-x)^2\cdot\sqrt{5(x-5)}\right)=\frac{8\sqrt{5}}{3}\left((10-x)^2\cdot\sqrt{(x-5)}\right)$