How do you take the partial derivative of this monster?

  • Thread starter Raziel2701
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  • #1
128
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[tex]e^{10x -x^2 +4y -y^2}[/tex]

I don't know where to start. I have a gut feeling this might require the chain rule, but I don't know how to use it on this thing. I tried doing some silly simplification which resulted in a pair of quotients and products of exponentials and tried to derive those using the quotient rule but it didn't work.

In any case, I need to find the first and second partial derivatives. How do I go about finding them?
 

Answers and Replies

  • #2
307
3
Hey Raziel,

Try rewriting a more general (and less messy expression) like:

[tex]e^{10x -x^2 +4y -y^2} = e^{f(x,y)}[/tex]

Taking the partial derivative (w.l.o.g. with respect to x) of the above expression is just taking the derivative of the expression with respect to x while holding y constant. In other words, what is,

[tex]\frac{d}{dx}e^{f(x)}\mathrm{?}[/tex]

If you know this piece of information, then you should be able to evaluate,

[tex]\frac{\partial}{\partial x}e^{f(x,y)},[/tex]

since they follow the same evaluation process.
 
  • #3
128
0
Got it, thanks.
 

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