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MHT CET202615 April 2026Evening ShiftMathematicsDifferentiationActual

The derivative of ( ( x+3 x ) ) is

Options

  1. A3 x+3 ( ( x+3 x ) )
  2. B3 x(x+3) ( ( x+3 x ) )
  3. C-3 x(x+3) ( ( x+3 x ) )
  4. D-1 x(x+3) ( ( x+3 x ) )

Correct answer

C. -3 x(x+3) ( ( x+3 x ) )

Step-by-step solution

Let y = ( ( x+3 x ) ) Using the chain rule, differentiating with respect to x gives: dy dx = ( ( x+3 x ) ) d dx ( ( x+3 x ) ) dy dx = ( ( x+3 x ) ) d dx ( (x+3) - x) dy dx = ( ( x+3 x ) ) ( 1 x+3 - 1 x ) dy dx = ( ( x+3 x ) ) ( x - (x+3) x(x+3) ) dy dx = -3 x(x+3) ( ( x+3 x ) )

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