JEE Main2009MathematicsDifferentiationActual

Let y be an implicit function of x defined by x^ 2 x -2 x^x y-1=0 . Then y^ (1) equals

Options

A-1
B1
C2
D- 2

Correct answer

A. -1

Step-by-step solution

x^ 2 x -2 x^x y-1=0 Now x=1 , 1-2 y-1=0 y=0 y= 2 Now differentiating eq. (1) w.r.t. ' x ' 2 x^ 2 x (1+ x)-2 [x^x (- cosec ^2 y ) d y d x + y x^x(1+ x) ]=0 Now at (1, 2 ) aligned & 2(1+ 1)-2 (1(-1) ( d y d x )_ (1, 2 ) +0 )=0 & 2+2 ( d y d x )_ (1, 2 ) =0 ( d y d x )_ (1, 2 ) =-1 aligned

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