Differentiate the following function from first principles

f(x)= 5x/(3-x)

1 answer

just plug and chug
f(x+h) - f(x) = 5(x+h)/(3-x-h) - 5x/(3-x)
= (5(x+h)(3-x) - 5x(3-x-h)) / (3-x-h)(3-x)
= 15h / (3-x-h)(3-h)
Now divide by h and you have
15 / (3-x-h)(3-x)
Now take the limit as h->0 and you have
15/(3-x)^2