# Math Help - Partial Derivative Simplification.

1. ## Partial Derivative Simplification.

The following image shows my confusion:

I don't have any trouble doing the derivative, but how did they arrive from the second-last line to the last?

I know that sin^2(x) + cos^2(x) = 1, but I can't see how to relate that here.

2. Originally Posted by scorpion007
The following image shows my confusion:

I don't have any trouble doing the derivative, but how did they arrive from the second-last line to the last?

I know that sin^2(x) + cos^2(x) = 1, but I can't see how to relate that here.
Since you were told that ${\color{red}x}={\color{red}r\cos\theta}$ and ${\color{blue}y}={\color{blue}r\sin\theta}$, we see that:

$y\left(-{\color{blue}r\sin\theta}\right)+x\left({\color{re d}r\cos\theta}\right)=y\left(-{\color{blue}y}\right)+x\left({\color{red}x}\right )=x^2-y^2$

3. Ahh! Oops. Of course Thank you.