# Thread: diff implicit functn

1. ## diff implicit functn

Find $\displaystyle \frac {\delta y}{\delta x} \, \left ( e^{-y} \right )$,

$\displaystyle = e^{-y} \cdot - \frac {\delta y}{\delta x}$

$\displaystyle = -e^{-y} \cdot \frac {\delta y}{\delta x}$, is this correct?

2. Originally Posted by ashura
Find $\displaystyle \frac {\delta y}{\delta x} \, \left ( e^{-y} \right )$,

$\displaystyle = e^{-y} \cdot - \frac {\delta y}{\delta x}$

$\displaystyle = -e^{-y} \cdot \frac {\delta y}{\delta x}$, is this correct?
Looks correct.
(As long as $\displaystyle y$ is a differenciable function )

This is my 36th Post!!!

3. Originally Posted by ashura
Find $\displaystyle \frac {\delta y}{\delta x} \, \left ( e^{-y} \right )$,

$\displaystyle = e^{-y} \cdot - \frac {\delta y}{\delta x}$

$\displaystyle = -e^{-y} \cdot \frac {\delta y}{\delta x}$, is this correct?
I don't know what conventions you have been taught, but to me your
notation doesn't mean anything.

It looks as though you are asked to find:

$\displaystyle \frac{d}{dx} e^{-y}$,

for which:

$\displaystyle \frac{d}{dx} e^{-y} = \frac{dy}{dx}\left(\frac{d}{dy}e^{-y}\right)=-e^{-y}\, \frac{dy}{dx}$.

RonL

4. Originally Posted by CaptainBlack
I don't know what conventions you have been taught, but to me your
notation doesn't mean anything.

It looks as though you are asked to find:

$\displaystyle \frac{d}{dx} e^{-y}$,

for which:

$\displaystyle \frac{d}{dx} e^{-y} = \frac{dy}{dx}\left(\frac{d}{dy}e^{-y}\right)=-e^{-y}\, \frac{dy}{dx}$.

RonL
Given the nature of the derivative it's probably not the same, but in Quantum we use that symbol for a functional derivative.

-Dan

5. Thanks for the correction Ronl.