Explanation The technique of logarithm differentiation is used where the function is composed of a product of functions so that logarithm transform will turn it into sum of functions which is easier to differentiate. For example, Let a function is f ( x ) = ( x + 5 ) ( x + 7 ) . Take logarithm on both side of the above function. ln [ f ( x ) ] = ln [ ( x + 5 ) ( x + 7 ) ] = ln ( x + 5 ) + ln ( x + 7 ) Differentiate the above function with respect to x , 1 f ( x ) f ′ ( x ) = 1 x + 5 + 1 x + 7 f ′ ( x ) = f ( x ) [ 1 x + 5 + 1 x + 7 ] = ( x + 5 ) ( x + 7 ) [ 1 x + 5 + 1 x + 7 ] = ( x + 7 ) + ( x + 5 ) Further, solve the above expression, f ′ ( x ) = 2 x + 12 The technique of logarithm differentiation is also used where a power function of variables or functions. For example, Let a function be f ( x ) = ( x + 5 ) ( x + 7 )

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