If y=x+sin(xy), then dy/dx =

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- Apr 6th 2008, 06:39 AMandrewsxderivative problem help
If y=x+sin(xy), then dy/dx =

Thank you - Apr 6th 2008, 06:46 AMbobak
use the chain and product rule on $\displaystyle \sin {xy} $

note $\displaystyle (xy)' = x \frac{dy}{dx} + y $

so $\displaystyle (\sin {xy})' = \left(x \frac{dy}{dx} + y\right) \cos {xy}$

can you finish this off ?

Bobak - Apr 6th 2008, 06:48 AMJhevon
use implicit differentiation. note that you will need the product rule when differentiating xy. whenever you differentiate a y-term, attach y' to it (y' is another notation that means dy/dx in this context). try it (of course, you should also be aware that you are going to differentiate sin(xy) using the chain rule)

EDIT: Oh well, bobak beat me to it. and with a more specific answer