InterviewSolution
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InterviewSolution
| 1. |
Let y be an implicit function of x defined by `x^(2x) -2x^xcoty-1=0`.Then y (1) equals` |
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Answer» at x= 1`1-2 xx1 cot y - 1 = 0` `cot y =(1-1)/-2 = 0` `y= pi/2` `y = x^(2x) ` `ln y = 2x ln x ` `d(v v )/dx = v (dv)/dx + v (dv)/dx` so,`1/y dy/dx = 2 ln x + 2` `dy/dx= 2y(ln x+1) ` `= 2x^(2x) [ln x +1]` `x^(2x) - 2x^xcot y - 1 = 0` `2x^(2x) (ln x+1) - 2[ x^x(ln x + 1)cot y + x^x(-cosec^2 y)dy/dx]= 0` x=1; `2 xx 1(0+1) - 2[ 1 xx1xx0 + 1(-1) dy/dx] = 0` `2 + 2 dy/dx = 0` `dy/dx = -2/2 = -1` option 1 is correct |
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