Find the marginal cost at the given production level x and s

Find the marginal cost at the given production level x, and state the units of measurement.

c(x)=15,000+100x+1,000/x. ; x=100

Solution

the marginal cost is the derivative of the cost function

hence

m(x) [marginal cost] = 0 + 100 - 1000/x^2

since derivative of x^n = nx^(n-1)

plugging in x =100

0+100 -0.1

99.90

and

units are dollars per production-level-unit. (assuming cost is in dollars)