For the first one I get
using the chain rule (twice)
and for the second notice
tan^5(x)sec^3(x) = sin^5(x)/cos^8(x)
so differentiating using the quotient rule, I get
(5sin^4(x)cos^9(x) + 8cos^7(x)sin^6(x))/cos^16(x)
which will cancel down a bit.