# Thread: Figuring out the derivative

1. ## Figuring out the derivative

I'm new to Calculus and totally lost on this problem.

Find the marginal revenue function if

R(x) = x(5+(10/x^1/2))

I understand it's the derivative of the above function, but I'm totally lost as to which rule needs to be applied.

Thanks!

2. Originally Posted by dasani
I'm new to Calculus and totally lost on this problem.

Find the marginal revenue function if

R(x) = x(5+(10/x^1/2))

I understand it's the derivative of the above function, but I'm totally lost as to which rule needs to be applied.

Thanks!
You will need the power rule for this problem.

The power rule says: $\displaystyle \frac {d}{dx}x^n = nx^{n - 1}$ for $\displaystyle n \neq 0$

$\displaystyle R(x) = x \left( 5 + \frac {10}{x^{1/2}} \right)$ ......expand

$\displaystyle \Rightarrow R(x) = 5x + 10x^{ \frac {1}{2}}$ ......now take the derivative

$\displaystyle \Rightarrow R'(x) = 5 + \frac {1}{2} \cdot 10 x^{ \frac {1}{2} - 1}$

$\displaystyle \Rightarrow R'(x) = 5 + 5x^{- \frac {1}{2}} = 5 + \frac {5}{\sqrt {x}}$

3. Thank you so much!