InterviewSolution
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InterviewSolution
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If ` x^(p) + y^(q) = (x + y)^(p+q) , " then" (dy)/(dx)` isA. ` - ( x ) /( y ) `B. ` ( x ) /( y ) `C. `- ( y ) / ( x ) `D. ` ( y ) /( x ) ` |
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Answer» Correct Answer - D if ` x ^p + y ^ q = ( x + y ) ^ ( p + q ) ` Taking log on both sides , ` p log x + q log y = ( p + q ) log ( x + y ) ` On differentiating w.r.t x, we get `( p ) /( x ) + ( q ) /( y ) * ( dy ) /( dx ) = (( p + q ))/( ( x + y)) ( 1 + (dy ) /(dx )) ` ` { (p) / ( x ) - ( p+ q )/( x + y )} = { ( p + q )/( x + y ) - ( q )/( y ) } (dy ) /( dx ) ` ` { ( px + py - px - qx ) /( x ( x + y ))} = { ( py + qy - qx - qy ) /( y ( x + y ))} (dy)/(dx ) ` ` rArr (( py - qx ) ) /( x ) = ((py- qx ) ) / (y ) * ( d y ) / ( dx ) ` `rArr ( dy)/ (dx ) = (y )/ ( x ) ` |
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