Question

Find the derivative of the function

1)f(t)=tan(e^2t)+e^tan2t
f'(t)=

[im not quite sure with this. im assuming the implicit differentiation]

2) F(t)=e^(8tsin2t)

[for this one i got 2e^(8t)(4sin(2t)+cos(2t)) but it is incorrect.

Answer 1

1) f'(t)=2*e^2t*(sec(e^2t))^2 + 2*e^tan2t*(sec(2t))^2

2)F'(t)=e^(8tsin2t)*(8sin2t+18tcos(2t))

Answer 2

#1: no impliocit, just use the chain rule

f=tan(u) + e^v
f' = sec^2(u) u' + e^v v'
= sec^2(e^2t) * 2e^2t + e^(tan2t) * sec^2(2t) * 2

#2: f = e^u
f' = u^u u'
= e^8tsin2t * (8sin2t + 16tcos2t)