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How do you find the partial derivative of #f(x,y) = xe^y + ye^x#?

Answer 1

First, you must bear in mind the rules for deriving #e#: the derived form of #e^f(x)# is #f(x)e^f(x)#.

The partial derivative for #x# is:

#e^y# + #y.e^x.1#

(note that the number 1 here refers to deriving the #x# in the second element of the function - no need to put that in your answer, it's jut to clear things out)

The partial derivative for #y# is:

#x.e^y.1# + #e^x#

Same logic here :)

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Answer 2

Emma Aldridge

To find the partial derivatives of ( f(x,y) = xe^y + ye^x ):

[ \frac{\partial f}{\partial x} = e^y + ye^x ]

[ \frac{\partial f}{\partial y} = xe^y + e^x ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.