Thread: Partial differentiation

How do I do the partial differentiation of following:

F(x,y)=(1-e^-x)(1-e^-y)

they has answer of e^-(x+y)

Originally Posted by Judi

How do I do the partial differentiation of following:

F(x,y)=(1-e^-x)(1-e^-y)

they has answer of e^-(x+y)

The partial derivative with respect to what variable?

(del F)/(del x) = e^{-x} * (1 - e^{-y}) <--- This is the partial derivative of F(x,y) wrt x.

(del F)/(del y) = (1 - e^{-x}) * e^{-y} <--- This is the partial derivative of F(x,y) wrt y.

neither of which is e^-(x+y). I'm not sure what you are asking for.

-Dan

Originally Posted by Judi

d^2
----- F(x,y)=e^(-(x+y))
dx dy

I am trying to see how this is possible, how the left hand side is equal to the right hand side

Thank you,

Ah! I didn't look at second derivatives. Okay, we can do this two ways:
(del F)/(del x) = e^{-x} * (1 - e^{-y}) (Apparently I missed a minus sign in my original response. I'll fix it.)

So taking del/(del y) of this:
(del^2 F)/(del x del y) = e^{-x}*e^{-y} = e^{-x - y}

or
(del F)/(del y) = (1 - e^{-x}) * e^{-y}

So taking del/(del x) of this:
(del^2)/(dex y del x) = e^{-x}*e^{-y} = e^{-x - y}

If you are having a problem doing the partial derivatives, remember that when you do a "del/(del x)" you hold all variables other than x constant. So, for example in (del F)/(del x) we hold the y constant, so effectively we are taking the derivative of (1 - e^{-x})* constant = e^{-x}*constant.

If you need more help than that with the derivatives, just let me know and I'll work up a quick tutorial for you.

-Dan

Thank you, thank you, thank you

Originally Posted by Judi

Thank you, thank you, thank you

You're welcome welcome welcome!

-Dan