GATE (TF) Textile 2008 Question Paper Solution | GATE/2008/TF/21

Question 21 (Textile Engineering & Fibre Science)

The total derivative of a function u=f(x,y,z) is expressed as du=\frac{\partial f}{\partial x}dx+\frac{\partial f}{\partial y}dy + \frac{\partial f}{\partial z} dz. If u=exp(x^2+y^2)\sin z, then the expression for du is given by

(A)du=exp(x^2+y^2)[2xdx + 2ydy]\cos z + \sin z \;dz
(B)du=exp(x^2+y^2)[2xdx + 2ydy]\sin z + \cos z \;dz
(C)du=exp(x^2+y^2) [(2xdx+2ydy)\cos z + \sin z \; dz]
(D)du=exp(x^2+y^2) [(2xdx+2ydy)\sin z + \cos z \; dz]
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