# Thread: differentiate question

1. ## differentiate question

How can u differentiate that :

c= 100,000* (x^2 + 25 )^0.5 + 75,000(8-x)

thnx

2. dc/dx=100,000*0.5*(x^2+25)^(-0.5).2.x+75,000(-1)

3. Originally Posted by Pulock2009
dc/dx=100,000*0.5*(x^2+25)^(-0.5).2.x+75,000(-1)

thnx , that is what I got

but I'm confused how to get the critical value of x

how can that equation be simplified in order to get the value of x

thnx again

4. dc/dx=0 and solve ,friend!!!

5. Originally Posted by Pulock2009
dc/dx=0 and solve ,friend!!!
the first part is raised to the power 0.5 which is kind of problem for me

any suggestion ?

6. A power of 0.5 is the same as taking a square root. So: $a^{0.5} = a^{1/2} = \sqrt{a}$

If it is negative: $a^{-0.5} = a^{-1/2} = \frac{1}{a^{1/2}} = \frac{1}{\sqrt{a}}$

Does that help?

7. Originally Posted by zisi
the first part is raised to the power 0.5 which is kind of problem for me

any suggestion ?
Surely you know that the derivative of $x^n$ is $nx^{n-1}$. That's true for n any number. Even 0.5.

The derivative of $x^{0.5}$ is $0.5x^{-0.5}$ which, as drumist points out, could also be written $\frac{0.5}{\sqrt{x}}$.

However, if the original problem was given as $x^{0.5}$ then I would recommend writing the answer in the same way: $0.5x^{-0.5}$.