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17 June, 23:25

Which of the following represents dy/dx when y = e-2x sec (3x) ?

A. 3e - 2x sec (3x) tan (3x) - 2xe-2x sec (3x)

B. 3e - 2x sec (3x) tan (3x) - 2e-2x sec (3x)

C. 3e - 2x sec (3x) tan (x) - 2xe-2x sec (3x)

D. 3e - 2x sec (3x) tan (x) - 2e-2x sec (3x)

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Answers (1)
  1. 18 June, 01:52
    0
    Using the product rule, which states that (uv) ' = u'v + uv':

    If y = (e^-2x) (sec3x)

    y' = (e^-2x) ' (sec3x) + (e^-2x) (sec3x) '

    y' = - 2 (e^-2x) (sec3x) + (e^-2x) (3 sec3x tan3x)

    y' = 3 (e^-2x) (sec3x tan3x) - 2e^-2x (sec3x)

    This matches choice B.
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Home » Mathematics » Which of the following represents dy/dx when y = e-2x sec (3x) ? A. 3e - 2x sec (3x) tan (3x) - 2xe-2x sec (3x) B. 3e - 2x sec (3x) tan (3x) - 2e-2x sec (3x) C. 3e - 2x sec (3x) tan (x) - 2xe-2x sec (3x) D. 3e - 2x sec (3x) tan (x) - 2e-2x sec (3x)
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