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If f(x) = \(e^{4\log_ex}\), then what is the derivative of f(x) ?

  1. \(e^{4\log_ex}\)
  2. \(\rm \frac {e^{4log_e x}}{x}\)
  3. 4x3
  4. None of these

Answer (Detailed Solution Below)

Option 3 : 4x3
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Detailed Solution

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Calculations:

Given, f(x) = \(e^{4\log_ex}\)

f(x) = \(\rm e^{\log_e {x^4}}\)

f(x) = x4               (∵ eloge x = x)

Taking derivative w. r. to x on both side, we get 

f'(x) = 4x3

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