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KCET2016MathematicsDifferentiation

The differential coefficient of ( ₁₀ x ) with respect to ( _ x 10 ) is

Options

  1. A( 1 )
  2. B( - ( ₁₀ x )² )
  3. C( ( _ x 10 )² )
  4. D( x² 100 )

Correct answer

B. ( - ( ₁₀ x )² )

Step-by-step solution

Let ( y= ₁₀ x ) and ( z= _ x 10 ) We know that, ( _ a b= b a ) So, ( y= x 10 ) and ( z= 10 x ) Thus, ( y= 1 z ) ( d y d z = -1 z² =- ( 1 z )²=-y² ) ( d y d x =- ( ₁₀ x )² )

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