Differentiate the function

Question

f(x)= e^x/x^2

Answer 1

f(x)= (e^x) / (x^2)

Apply derivative each side with respect to x.

d/dx (f(x))= d/dx (e^x / x^2)

Apply quotient rule : d/dx (u/v) = [v d/dx(u) - u d/dx(v)]/ v²

f'(x) = [ x^2 d/dx(e^x) - (e^x) d/dx(x^2)] / (x^4)

f'(x) = [ x^2(e^x) - e^x(2x)] / (x^4)

f'(x) = { x(e^x) [x - 2] } / (x^4)

Cancel common terms.

f'(x) = {(e^x) ( x - 2)} / (x^3)