Hi folks, hopefully this is in the right forum. My textbook tells me I can use the product rule to go from the functions x = r cos phi and y = r sin phi to find expressions for dx and dy. I'm not clear whether this is partial differentiation (I thought I understood that!), or what I am differentiating with respect to! I have attached a jpg of the textbook section which should be clearer that typing it all out. I think I can get to the final expression, it's finding the middle two I don't understand. Can anyone help?

My jpg refers to equation 3.4, this is simply dl^2 = dx^2 + dy^2.