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Find the derivative of 2-3x with respect to x

  1. 2-3x
  2. 3log 2 × 2-3x
  3. -3 × 2-3x
  4. (-3log 2) × 2-3x

Answer (Detailed Solution Below)

Option 4 : (-3log 2) × 2-3x
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Detailed Solution

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Concept:

Formula:

log mn = n log m

 

Calculation:

Let y = 2-3x

Taking log both sides, we get

⇒ log y = log 2-3x

⇒ log y = -3x log 2           (∵ log mn = n log m)       

⇒ log y = (-3log 2) x

differentiating with respect to x

⇒  = (-3log 2) × 1

⇒  = (-3log 2)y

∴   = (-3log 2)2-3x

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