Question

Let $y=e^{\frac{1}{x}}$ then find $\frac{d^{2}y}{d{x}^2}$.

Answer 1

Given $y=e^{\frac{1}{x}}$.

Now differentiating both sides with respect to $x$ we get,

$\frac{dy}{dx}=$ $e^{\frac{1}{x}}.-\frac{1}{x^2}$

Now again differentiating both sides with respect to $x$ we get,

$\frac{d^{2}y}{d{x}^2}=$ $e^{\frac{1}{x}}.\frac{1}{x^4}$ $+e^{\frac{1}{x}}.\frac{2}{x^3}$.