# Thread: can u fin the derivative of this function

1. ## can u fin the derivative of this function

i need the derivative of :

2. Originally Posted by geriniki
i need the derivative of :

First simplify the power: $\frac{1}{x}\left(x-\frac{1}{x}\right)=1-\frac{1}{x^2}$ , and now apply the chain rule to $\left(e^{f(x)}\right)'=f'(x)\cdot e^{f(x)}$ ...

Tonio

3. The solution you provided doesn't match the problem.

Can I ask what solution you arrived at?

4. this must be solution it's in the textbook :/
sorry i haven't written it correctly = x - 1/x isn't in the power

5. Is this the correct function?

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

6. yes

7. You may use the product rule:

$f'(x) = e^{1/x} \cdot \left(x-\frac{1}{x}\right)' + \left(e^{1/x}\right)' \cdot \left(x-\frac{1}{x}\right)$

Can you find the derivatives of $x-\frac{1}{x}$ and $e^{1/x}$?

8. yes thank you

9. Do you see why Tonio was confused? (Because he never gives a wrong answer!)

What you gave in your initial post was $e^{\frac{1}{x}\left(x- \frac{1}{x}\right)}$ not $e^{\frac{1}{x}}\left(x- \frac{1}{x}\right)$.