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Manipal MET2019MathematicsDifferentiation

Derivative of the function f(x)= ₅ ( ₇ x ), x 7 is

Options

  1. A1 x( 5)( 7) ( ₇ x )
  2. B1 x( 5)( 7)
  3. C1 x( x)
  4. DNone of the above

Correct answer

A. 1 x( 5)( 7) ( ₇ x )

Step-by-step solution

Given that, f(x)= ₅ ( ₇ x ) or it can be written as f(x)= _e ( ₇ x ) _e 5 [ _a b= b a ] On differentiating with respect to x , we get Now, aligned f^ (x) & = 1 _e 5 [ 1 ₇ x d d x ( ₇ x ) ] & = 1 _e 5 1 ₇ x 1 _e 7 1 x & = 1 x( 5)( 7) ( ₇ x ) aligned

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