When to assign a value to a multiple chain derivative?

[Nano-Passion]

I was doing my homework and I ran into a problem of a chain rule within a chain rule. When do I know what to assign a value? For example:

y=e^{-x^2}

When I assign u=e^{-x} and y=u^2 I get a wrong value. According to cramster I was supposed to assign y = e^u and u=-x^2. But when am I supposed to know what value to assign? For clarification let me write out the steps my problem.

y=e^{-x^2}
u=e^{-x} -----> \frac{du}{dx}=-e^{-x}
y=u^2 ---------> \frac{dy}{du}=2u
This shows out that the chain is consistent.
\frac{dy}{dx}=\frac{dy}{du}\frac{du}{dx}<br /> =2u(-e^{-x})<br /> =2(e^{-x})(-e^{-x})<br /> =-2e^{-2x}<br /> <br /> But cramster has a different answer. Cramster assigned the values as y=e^u and u =-x^2 got an answer of:<br /> =-2x^{-x^2}

 

[gb7nash]

When I assign u=e^{-x} and y=u^2 I get a wrong value.

This is your problem. u^{2} is not equal to e^{-x^2}. In fact, it's equal to e^{-x}e^{-x} = e^{-2x}

 

[Nano-Passion]

This is your problem. u^{2} is not equal to e^{-x^2}. In fact, it's equal to e^{-x}e^{-x} = e^{-2x}

No I assign y=u^2. So then f&#039;(y)=2u

Edit: I think there is a bit of a confusion. This is the answer I got-->e^{-x} = e^{-2x}. I think you confused it with my last line; the last line is the answer posted up on cramster. I edited my original post and clarified it.

 

[gb7nash]

No I assign y=u^2

Is this the same y as:

y=e^{-x^2}

?

 

[Nano-Passion]

Read my previous post I edited it, it might clarify things. Basically when there is a chain rule within a chain rule I assign a value. Where in this case it was:

y=u^2 and u=e^{-x}

Ohhhhh.. so in this case u^2 implies the function (e^{-x})^2 Where it is supposed to be only -x^2

That is what your saying right? Because I just noticed.

 

[gb7nash]

Ohhhhh.. so in this case u^2 implies the function (e^{-x})^2 Where it is supposed to be only -x^2

That is what your saying right? Because I just noticed.

Correct