Find the derivative of

Question

4 sec^7 (πt − 6)?

Answer 1

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)