differentiating in terms of y and x

**George321** · April 15th 2010, 03:01 AM

Given that
$siny=xy+x^2$
find dy/dx in terms of $x$ and $y$

Plese talk me through how to do this.
Thanks

**mr fantastic** · April 15th 2010, 03:10 AM

Originally Posted by George321

Given that
$siny=xy+x^2$
find dy/dx in terms of $x$ and $y$

Plese talk me through how to do this.
Thanks

Have you been taught implicit differentiation? There are many threads in this subforum that cover questions like this one. Use the Search tool to find them, read them and then make another attempt on this question. You should also review the examples in your class notes and textbook.

Please post your work and say where you are stuck if you need more help after doing this.

Here is a small start:

From the product rule:

$\frac{d (xy)}{dx} = y + x \frac{dy}{dx}$ .

From the chain rule:

$\frac{d (\sin y)}{dx} = \frac{d (\sin y)}{dy} \cdot \frac{dy}{dx}$ .