Math Help - 1st and 2nd derivatives of y=e^(1/(x^2))

1. 1st and 2nd derivatives of y=e^(1/(x^2))

for the first derivative i got:

y'=(-2e^1/(x^2)) /x^3

2nd one i got:

(4x^3e^1/(x^2) + 6x^2e^1/(x^2)) / x^6

are they correct? if not, what are the correct answers...?

thank you in advance

2. Originally Posted by LandLBoy
for the first derivative i got:

y'=(-2e^1/(x^2)) /x^3

2nd one i got:

(4x^3e^1/(x^2) + 6x^2e^1/(x^2)) / x^6

are they correct? if not, what are the correct answers...?

thank you in advance
Dear LandLBoy,

The first derivative is correct. But the second derivative should be,

$\frac{d^{2}y}{dx^2}=\frac{4e^{\frac{1}{x^2}}+6x^{2 }e^{\frac{1}{x^2}}}{x^6}$