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

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Answer 1 · 2017-10-15T13:32:29

$dy/dx =-e^(1/x)/x^2$

Use the chain rule by posing $u = 1/x$ , so that $y=e^u$ :

$dy/dx = dy/(du) (du)/dx = d/(du) e^u xx d/dx 1/x = e^u xx -1/x^2 =-e^(1/x)/x^2$

Answer 2 · 2017-10-15T13:39:27

Let's see.

Let the equation $y=e^(1/x)$ be a function of $x$ such that $rarr$

$y=f(x)=e^(1/x)$

Now, differentiating the equation w.r.t $x$ we get $rarr$

$dy/dx=d/dx(e^(1/x))$

$:.dy/dx=e^(1/x)cdotd/dx(1/x)$ $larr$ Chain Rule.

$:.dy/dx=e^(1/x)cdot(-1/x^2)$

$:.color(red)(dy/dx=-e^(1/x)/x^2)$ . (Answer).

Hope it Helps:)

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