Question 858133
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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) = {{{1000*sqrt(x^2-0.1x)}}}

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

R(x) = {{{1000*(x^2-0.1x)^(1/2)}}}

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) = {{{1000*(1/2)*(x^2-0.1x)^(-1/2)*(2x-0.1)}}}

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

R'(x) = {{{500*(2x-0.1)*(x^2-0.1x)^(-1/2)}}}

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
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