Question

f(x, y) = sin(x) + cos(y) + xy^2; x = cos(t); y = sin(t) Find ^df⁄dt at t = ^π⁄2

(a) 2

(b) -2

(c) 1

(d) 0

The question was asked in an interview.

This intriguing question originated from Partial Differentiation topic in division Partial Differentiation of Engineering Mathematics

Answer 1

Correct choice is (b) -2

Explanation: Using chain rule we have

\(\frac{df}{dt}=f_x.\frac{dx}{dt}+f_y.\frac{dy}{dt}\)

= (cos(x) + y^2).(-sin(t)) + (-sin(y) + 2xy).(cos(t))

Put t= ^π⁄2; we have x=0; y=1

=(1 + 1).(-1) + 0 = -2.