How can u differentiate that :
c= 100,000* (x^2 + 25 )^0.5 + 75,000(8-x)
thnx
Surely you know that the derivative of $\displaystyle x^n$ is $\displaystyle nx^{n-1}$. That's true for n any number. Even 0.5.
The derivative of $\displaystyle x^{0.5}$ is $\displaystyle 0.5x^{-0.5}$ which, as drumist points out, could also be written $\displaystyle \frac{0.5}{\sqrt{x}}$.
However, if the original problem was given as $\displaystyle x^{0.5}$ then I would recommend writing the answer in the same way: $\displaystyle 0.5x^{-0.5}$.