# How do you find the derivative of y=e^(1/x)?

Jul 30, 2014

$y ' = - {e}^{\frac{1}{x}} / \left({x}^{2}\right)$

Explanation :

Using Chain Rule,

Suppose, $y = {e}^{f} \left(x\right)$

then, $y ' = {e}^{f} \left(x\right) \cdot f ' \left(x\right)$

Similarly following for the $y = {e}^{\frac{1}{x}}$

$y ' = {e}^{\frac{1}{x}} \cdot \left(\frac{1}{x}\right) '$

$y ' = {e}^{\frac{1}{x}} \cdot \left(- \frac{1}{x} ^ 2\right)$

$y ' = - {e}^{\frac{1}{x}} / \left({x}^{2}\right)$