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

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

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

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