How do you derive...

• Nov 3rd 2012, 07:35 PM
asdfpjdfj
How do you derive this...?
HEY!
I'm new here and I was wondering how to derive something like:
Attachment 25538
I can do the chain and product rule however the 3 has confused me...

Any working would be appreciated (Bow)

Challenge accepted?
• Nov 3rd 2012, 09:42 PM
chiro
Re: How do you derive...
Hey asdfpjdfj.

d/dx (a*f(x)) = a*d/dx(f(x)).
• Nov 3rd 2012, 11:22 PM
hollywood
Re: How do you derive...
Yes, your function, $\displaystyle f(x)=\frac{8(10-x)^2\cdot\sqrt{5(x-5)}}{3}$ can be written $\displaystyle f(x)=\frac{1}{3}\left(8(10-x)^2\cdot\sqrt{5(x-5)}\right)$, so you use chiro's suggestion with $\displaystyle a=\frac{1}{3}$.

- Hollywood
• Nov 4th 2012, 04:25 AM
Plato
Re: How do you derive this...?
Quote:

Originally Posted by asdfpjdfj
HEY!
Attachment 25538
Any working would be appreciated
Challenge accepted?

I suggest writing it as:
$\displaystyle \frac{1}{3}\left(8(10-x)^2\cdot\sqrt{5(x-5)}\right)=\frac{8\sqrt{5}}{3}\left((10-x)^2\cdot\sqrt{(x-5)}\right)$