Derivative of (-y^2+6x^2)/2xy

Answer 1

Let F(x,y) = (-y² +6x²)/2xy. Simplify this as: F(x,y) = -y/(2x) + 3x/y.

Now dF(x,y) = [(∂F/∂x) dx + (∂F/∂y) dy] by the total derivative rule for multi (two) variable functions.

All we need to do is to calculate partial derivates of F with respect to x and y and replace in the above:

dF(x,y)= [3/y + y/(2x²) ] dx + [-3x/y² - 1/2x] dy = (3/y) [dx - (x/y) dy] - (1/2x) [ y/x dx+ dy].