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What is the derivative of f(x) = x²·sin(x)?
  1. 2x·cos(x)
  2. x²·cos(x)
  3. 2x·sin(x) + x²·cos(x)
  4. None of these
Explanation

This is a product of two functions, so we apply the product rule:

Here,

  • , so


  • v = sin(x)    , so v' = cos(x)

Now apply the rule:

f'(x) = 2x cdot sin(x) + x^2 cdot cos(x)

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