I don't really know how to do implicit differentiation. Could you show me how to do it with the equationy-sin(xy)=x²? Thanks!

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- Jan 10th 2010, 04:09 PMsuchgreatheightsImplicit Differentiation
I don't really know how to do implicit differentiation. Could you show me how to do it with the equation

**y-sin(xy)=x****²**? Thanks! - Jan 10th 2010, 04:41 PMmr fantastic
I assume the main trouble is to get $\displaystyle \frac{d \sin (xy) }{dx}$ (if it isn't then I suggest you go back and review the topic and then attempt some easier questions). First make the substitution $\displaystyle u = xy$ and use the chain rule:

$\displaystyle \frac{d \sin (xy) }{dx} = \frac{d \sin u}{du} \cdot \frac{du}{dx} = \cos u \cdot \frac{du}{dx} = \cos (xy) \cdot \frac{d (xy)}{dx}$.

I assume you can use the product rule to get $\displaystyle \frac{d (xy)}{dx} = y + x \frac{dy}{dx}$ and then put it all together. - Jan 10th 2010, 05:27 PMsuchgreatheights
Ok I get that but where does the first y fit in? What would be the final answer?

- Jan 10th 2010, 05:32 PMmr fantastic