Thread: Another calculating y'

1. Another calculating y'

If y=xe^(-1/x)

is y'= xe^(-1/x)*(-(x-1)/x^2)+e^(-1/x)

2. Originally Posted by spazzyskylar
If y=xe^(-1/x)

is y'= xe^(-1/x)*(-(x-1)/x^2)+e^(-1/x)

You said
d/dx(-1/x) = -(x-1) / x^2

3. Originally Posted by spazzyskylar
If y=xe^(-1/x)

is y'= xe^(-1/x)*(-(x-1)/x^2)+e^(-1/x)
?

note that the derivative of $-\frac{1}{x}$ is $\frac{1}{x^2}$

4. Not really, should it be -(x+1)/x^2

5. Not quite! if $u=-\frac{1}{x}$

$\frac{d}{dx}(xe^\frac{-1}{x})=\frac{d}{dx}xe^u=x\frac{d}{dx}e^u+e^u(1)$

$=x\frac{du}{du}\frac{d}{dx}e^u+e^u=x\frac{du}{dx}\ frac{d}{du}e^u+e^u$

$=(x)\frac{1}{x^2}e^u+e^u=\frac{e^\frac{-1}{x}}{x}+e^\frac{-1}{x}$

6. Originally Posted by spazzyskylar
If y=xe^(-1/x)

is y'= xe^(-1/x)*(-(x-1)/x^2)+e^(-1/x)
$u = x \: \rightarrow \: u' = 1$

$v = e^{-\frac{1}{x}} \: \: \rightarrow \: v' = \frac{1}{x^2}e^{-\frac{1}{x}}$

skeeter gave the derivative of the exponent so multiply due to the chain rule

Now use the product rule

y' = u'v + uv'

Spoiler:
$e^{-\frac{1}{x}} + \frac{1}{x}e^{-\frac{1}{x}} = e^{-\frac{1}{x}}\left(1+\frac{1}{x}\right)$

7. I got it now

8. $y'=x'e^{-1\over x} +x(e^{-1\over x})'$