Suppose that f(x)= (e^x)/(x^2+16. Find f'(0).

Answer 1

f'(x) = (e^x (x^2+16) - e^x (2x)) / (x^2+16)^2
= e^x(x^2-2x+16)/(x^2+16)^2
f'(0) = 16/16^2 = 1/16