U=2xy
what is
du/dx ?
u=2xy
du=2x dy + 2y dx
du/dx= 2x dy/dx + 2y
To find du/dx given u=2xy, we can use the chain rule of differentiation.
First, express u as a function of x and y: u = 2xy.
Now, differentiate both sides of the equation with respect to x, treating y as a constant:
du/dx = d/dx (2xy).
To differentiate 2xy with respect to x, we use the product rule, where the derivative of the first function (2x) is multiplied by the second function (y), plus the first function (2x) multiplied by the derivative of the second function (dy/dx):
du/dx = (2x * dy/dx) + (2y * dx/dx).
Since dx/dx is equal to 1, we can simplify the equation to:
du/dx = 2x * dy/dx + 2y.
Therefore, the derivative of u with respect to x is given by du/dx = 2x * dy/dx + 2y.