Find the derivative of the follwing function and explain the rules used:

p(x)= 100/1+99e^-.0725x

This function requires the use of the quotient rule, which states that:
f(x) = a/b [where a and b are functions of x]
f '(x) = (ba' - ab')/(b^2)

p(x) = 100/(1+99*e^(-0.0725*x))
a = 100
b = 1+99*e^(-0.0725*x)
a' = 0
b' = -7.1775*e^(-0.0725*x)

p '(x) = (100*(1+99*e^(-0.0725*x)))/(-7.1775*e^(-…
p'(x) = [100 + 9900*e^(-0.0725x)]/ (-7.1775*e^(-0.0725x))^2

Also, the derivative of the function:
f(x) = ce^(u(x))
f'(x) = c*e^(u(x))*(du/dx)
c is the function's coefficient
u(x) is a function of x
du/dx is the derivative of u(x)

There you go. Hope that helps.