1. ## Derivative

How do i find the derivitive with respect to x of:
w = (x^2)+(y/x)

AND with respect to y of the same equation.

So in other words dw/dx and dw/dy?

am confused how to differentiate y/x?

Thanks

2. Originally Posted by taurus
How do i find the derivitive with respect to x of:
w = (x^2)+(y/x)

AND with respect to y of the same equation.

So in other words dw/dx and dw/dy?

am confused how to differentiate y/x?

Thanks
When you are differentiating in respect to a certain variable you treat the ohter variables as constants

$\displaystyle \therefore\frac{dW}{dx}=2x-\frac{y}{x^2}$

Can you go from there?

3. Originally Posted by taurus
How do i find the derivitive with respect to x of:
w = (x^2)+(y/x)

AND with respect to y of the same equation.

So in other words dw/dx and dw/dy?

am confused how to differentiate y/x?

Thanks
For all we know y might depend on x and thats why I think it is more complete to say,

$\displaystyle w = x^2+\frac{y}{x} \Rightarrow \frac{dw}{dx} = 2x + \frac1{x}\frac{dy}{dx} - \frac{y}{x^2}$

$\displaystyle w = x^2+\frac{y}{x} \Rightarrow \frac{dw}{dy} = 2x \frac{dx}{dy} + \frac1{x} - \frac{y}{x^2}\frac{dx}{dy}$