Question

If u = x^x + y^y + z^z , find ^du⁄dx + ^du⁄dy + ^du⁄dz at x = y = z = 1.

(a) 1

(b) 0

(c) 2u

(d) u

This question was addressed to me in exam.

My question is taken from Partial Differentiation topic in section Partial Differentiation of Engineering Mathematics

Answer 1

Right choice is (d) u

To explain I would say: ^du⁄dx = x^x (1+log⁡(x))

^du⁄dy = y^y (1+log⁡(x))

^du⁄dz = z^z (1+log⁡(x))

At x = y = z = 1,

^du⁄dx + ^du⁄dy + ^du⁄dz = u.