Ex 5.5, 14 - Find dy/dx of (cos x)y = (cos y)x - Logarithmic Differentiation - Type 1

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  1. Chapter 5 Class 12 Continuity and Differentiability
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Ex 5.5, 14 Find of the functions in, ( cos ) = ( cos ) Given ( cos ) = ( cos ) Taking log both sides log ( cos ) = log ( cos ) . log ( cos )= . log ( cos ) Differentiating both sides . . . . ( . log ( cos )) = . log ( cos ) Finding ( . ( )) ( . ( )) = ( ) . log co + ( ( )) . = . log co + 1 . . = . log co + 1 . sin . = . log co + sin . = . log co tan . Finding . ( ) . ( ) = ( ) . log co + ( ( )) . = log co + 1 . . = log co + 1 . . . = log co + 1 . . . = log co + 1 . ( sin ) . . = log co + tan . . Now , ( . log ( cos )) = . log ( cos ) log co tan . = log co tan . . log co . tan = log co . tan . log co + tan = log co + tan log co + tan = log co + tan = + +

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