CalculusMath
posted by Lorine on .
Find the derivative of
4 sec^7 (πt − 6)?

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 t6)tan(pi t6)