sin(xy)=e^xy

should i use product or chain rule on the left side of the equation? I just started doing these and I am a bit confused. Thanks for any help

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- Apr 25th 2011, 05:59 PMjimbowickersmackhelp with implicit differentiation
sin(xy)=e^xy

should i use product or chain rule on the left side of the equation? I just started doing these and I am a bit confused. Thanks for any help - Apr 25th 2011, 06:03 PMAckbeet
Like an onion, you must peel back the layers, working from the outside in. That means chain rule first, with a product rule inside. On the RHS, is it (e^x)y or e^(xy)? You want to be explicit with parentheses.

- Apr 26th 2011, 04:42 AMbugatti79
For the left hand side may I ask Ackbeet: are you assuming that y is a function of x in order to use both the chain rule and product rule when differentiating wrt x?

I would have just use the chain rule and treat y as constant...? I mean having z=f(xy) doesnt mean that y is a function of x right? - Apr 26th 2011, 04:58 AMpoirot
The title is the clue bugatti.

Assuming you mean e^(xy), then you want d/dx(xy)*e^(xy). - Apr 26th 2011, 05:25 AMAckbeet
- Apr 27th 2011, 08:33 AMbugatti79
- Apr 27th 2011, 08:52 AMHallsofIvy