# Math Help - Help me to derivate!

1. ## Help me to derivate!

I've tried to derivate this function a couple of times but since I'm not very into all the rules I'm afraid I did it incorrect.

Will anyone tell me if this is right:

f(x)= (1/3)(pi)((xR/2pi)^2)((R^2)-((xR/2pi)^2))^0.5)

f'(x)= 1/3 * pi * (xR/2pi)^2
= (1/3)(pi)(2)(xR/2pi)(1/2pi)
= (1/3)(xR/2pi)
= xR/6pi

I'm sorry if it looks messy!

Thanks,

2. Do you mean;

$1/3 \pi \left( \frac{xR}{2 \pi} \right)^{2} (R^{2}- \sqrt( \left( \frac{xR}{2 \pi} \right)^{2}))$

is
$1/3 \pi \left( \frac{xR}{2 \pi} \right)^{2} (R^{2}- \left( \frac{xR}{2 \pi} \right) )$

3. Originally Posted by ninjajulez
I've tried to derivate this function a couple of times but since I'm not very into all the rules I'm afraid I did it incorrect.

Will anyone tell me if this is right:

f(x)= (1/3)(pi)((xR/2pi)^2)((R^2)-((xR/2pi)^2))^0.5)

f'(x)= 1/3 * pi * (xR/2pi)^2
= (1/3)(pi)(2)(xR/2pi)(1/2pi)
= (1/3)(xR/2pi)
= xR/6pi

I'm sorry if it looks messy!

Thanks,
$f(x)= \frac{\pi}{3} \left(\frac{xR}{2\pi}\right)^2 \left(R^2-\left(\frac{xR}{2\pi}\right)^2\right)^{\frac{1}{2} }$

$f(x)= \frac{\pi}{3} \cdot \frac{x^2R^2}{4\pi ^2} \cdot \left(R^2 - \frac{x^2R^2}{4\pi ^2} \right)^{\frac{1}{2}}$

$f'(x)=\frac{\pi}{3} \left(\frac{2xR^2}{4\pi ^2} \cdot \left(R^2 - \frac{x^2R^2}{4\pi ^2} \right)^{\frac{1}{2}}+\frac{x^2R^2}{4\pi ^2} \cdot\frac{1}{2} \left(\frac{-2xR^2}{4\pi ^2}\right)\cdot \left(R^2 - \frac{x^2R^2}{4\pi ^2} \right)^{\frac{-1}{2}} \right)$

I used this

$f(x) = g(x) \cdot h(x)$

$f'(x) = g'(x) \cdot h(x) + g(x) \cdot h'(x)$