99 Percentile Qs Bank for JEE MainMathematicsDifferentiation

If z= y x [ x y + (1+ y x ) ] , then x z x is equal to

Options

Ay z y
B-y z y
C2 y z y
D2 y z x

Correct answer

B. -y z y

Step-by-step solution

We have, z= y x [ x y + (1+ y x ) ] array r z x = y x [ x y 1 y - (1+ y x ) (- y x^2 ) ] + (- y x^2 ) [ x y + (1+ y x ) ] x z x =y [ 1 y x y + y x^2 (1+ y x ) ] - y x [ x y + (1+ y x ) ] x z x = x y + y^2 x^2 (1+ y x )-z array Similarly, y z y =- x y - y^2 x^2 (1+ y x )+z On adding Eqs. (i) and (ii) x z x =-y z y

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