Posted by **michelle** on Monday, October 8, 2012 at 11:35pm.

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.

- calculus -
**Arnold**, Tuesday, October 9, 2012 at 12:33am
1) f'(t)=2*e^2t*(sec(e^2t))^2 + 2*e^tan2t*(sec(2t))^2

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

- calculus -
**Steve**, Tuesday, October 9, 2012 at 5:01am
#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)

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