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

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 :confused: Please Help!

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

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

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

For the function you cite, we also need:

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

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

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

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

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.

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

Quotient rule! Thank you!