Question

What is the derivative of `f(x)=(e^(1/x))/x^2` ?

Answer 1

By Quotient Rule,

`f'(x)={-1/x^2e^{1/x}cdot x^2-e^{1/x}cdot2x}/{(x^2)^2}`

by cancelling out `x^2` in the numerator,

`={-e^{1/x}-2xe^{1/x}}/{x^4}`

by factoring out `-e^{1/x}` from the numerator,

`=-{(1-2x)e^{1/x}}/{x^4}`