Question

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)

Answer 1

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.