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Whats this mean?

i know the first term is \[e^t \cos (e^t)\]

What is a LGBADERIVATIVE?

derivative lol

Oh I would break it up
And use log differentiation

\[a = e^{\sin t}\]
\[\ln a = \sin t\]
\[a' = \sin t \cos t?\]

well for the first one we don't need log differentiation but the second one we do

Second will be:
\[\huge cost(e^{sint})\]

oops yeah that's what i meant

\[g=e^{\sin(t)}\]
\[\ln(g)=\ln(e^{\sin(t)})\]
Or you can use the short way whatever lol

\[\huge e^t \cos t + \cos t (e^{\sin t})\]

right?

No first one is not..

\[\huge e^t(cose^t)\]

oh argument is e^t

\[\huge e^t \cos (e^t) + \cos t(e^{\sin t})\]

Now it is okay..

wonderful