Hi there,

Your Problem:
A total revenue function is given by R(x)=1000 sq.rt x^2-0.1x
Find R'(x)

Solution:
R'(x) is the marginal revenue function (and the derivative of R(x).)

R(x) = 

When I want to take the derivative of a radical expression, I usually convert the radical to a fractional 
exponent, then differentiate.

R(x) = 

Now we differentiate using the Power Rule. We will also need to use the Chain Rule to differentiate the 
expression under the radical.

R'(x) = 

We can simplify this expression by multiplying (1000)(1/2) to give 500.

R'(x) = 

If you like you can rewrite the equation in radical form, but it's not necessary. Notice that the exponent 
is now -1/2, so the radical expression will be in the denominator.

I hope this helps. Feel free to email if you have a question about the solution.

Mrs. Figgy
math.in.the.vortex@gmail.com