Question

If u=tan⁻¹((y)/(x²)), then evaluate x(delu )/(delx )+y(delu )/(dely ).

Answer 1

To evaluate x(delu )/(delx )+y(delu )/(dely ), we can calculate the partial derivatives of u with respect to x and y, substitute these into the expression, and simplify the result.

Step-by-step explanation:

To evaluate the expression x(delu )/(delx )+y(delu )/(dely ), we first need to find the partial derivatives of u with respect to x and y.

Given that u = tan⁻¹(y/x²), we can calculate the partial derivatives as follows:

delu / delx = -y/(x²+y²)
delu / dely = 1/(x²+y²)

Now, we substitute these partial derivatives into the expression:

x(delu )/delx + y(delu )/dely = x(-y/(x²+y²)) + y(1/(x²+y²))
After simplifying the expression, we get:

x(-y/(x²+y²)) + y(1/(x²+y²)) = (-xy+y)/(x²+y²) = -xy/(x²+y²)