GATE Electronics and Communications (EC) 2020 Solved Papers

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Question : 33 of 65

Marks: +1, -0

The partial derivative of the function

{F}( {x}, {y}, {z})= {e}^{1- {x} \cos {y}}+ {xze}^{-1 {/}(1+ {y} 2)}

With respect to

x

at the point

(1,0, e)

is

1
$\;{1}/{ {e}}$
0
$-1$

Solution:

\;{∂ f}/{∂ x}=e^{(1-x \cos y)}(-\cos y)+z e^{(-\;{1}/{1+y 2})}

(\;{∂ f}/{∂ x})_{(1,0, e)}=e^{0}(-1)+e e^{-1}

=-1+1=0

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