Problem: Let Y = cosx + sinx / cosx - sinx. Find dy/dc

**TripShip** · January 25th 2013, 08:39 AM

Having trouble finding the answer to this question:

Let Y = cosx + sinx / cosx - sinx

Find dy/dx

The answer is supposed to be (cosx - sinx)(-sinx + cosx)-(cosx + sinx)(-sinx - sinx) / (cosx-sinx)^2 which can be simplified further

But I have no idea how this is gotten

Please Help!

**MarkFL** · January 25th 2013, 08:55 AM

You have a minor typo in your intended result, but it is obtained by using the quotient rule:

$\frac{d}{dx}\left(\frac{f(x)}{g(x)} \right)=\frac{f'(x)g(x)-f(x)g'(x)}{g^2(x)}$

For the function you cite, we also need:

$\frac{d}{dx}(\sin(x))=\cos(x)$

$\frac{d}{dx}(\cos(x))=-\sin(x)$

**AZach** · January 25th 2013, 08:58 AM

I got $y' = \frac{(-sinx+cosx)(cosx-sinx)-(cosx+sinx)(-sinx-cosx)}{(cosx-sinx)^2}$

Remember that the numerator and denominators are quantities, and you need to take the derivative of the top and bottom quantities in accordance with the quotient rule.

**TripShip** · January 25th 2013, 09:04 AM

Quotient rule! Thank you!

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Re: Problem: Let Y = cosx + sinx / cosx - sinx. Find dy/dc

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