Math Help - derivative of e^(cost + lnt)

y= e^(cost + lnt)

then i tired:
y= e^cost - e^lnt
lny=lne^cost- lne^lnt
(where lne crosses out)
lny=cost-lnt
1/y y' =-sint - 1/t
y' = e^cost- e^lnt (-sint - 1/t)

but the answer is: e^cost (1- tsint)

Originally Posted by genlovesmusic09

y= e^(cost + lnt)

then i tired:
y= e^cost - e^lnt ---------> this is wrong

y= e^(cost + lnt) = e^(cos t) * e^(ln t)

Do you know what e^(ln t) equals to ? Then you can use the prroduct rule for derivative.