Calculus-Math

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Find the derivative of
4 sec^7 (πt − 6)?

  • Calculus-Math -

    well, we know we keep the 4 :)

    Let z = 4(sec u)^7 and u = pi t - 6
    then
    dz/du = 4 * 7 (sec u)^6 d sec u/du

    = 28 (sec u)^6 (sec u )(tan u)

    = 28 sec^7 u tan u
    dz/dt = dz/du * du/dt = dz/du * pi
    so
    dz/dt = 28 pi sec^7(pi t-6)tan(pi t-6)

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