How do you differentiate $y=tlog3e^sint$ ?

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Answer 1 · 2017-04-26T18:05:32

Please see the explanation.

Given: $y=tlog(3e^sin(t))$

Using the property $log(a^c) = (c)log(x)$

$y = tsin(t)log(3e)$

Differentiate:

$dy/dt = d/dttsin(t)log(3e)$

Use the property that the derivative is a linear operation:

$dy/dt = log(3e)d/dttsin(t)$

$dy/dt = log(3e)(dt/dtsin(t) + td/dtsin(t))$

Simplify:

$dy/dt = log(3e)(sin(t) + tcos(t))$

How do you differentiate y=tlog3e^sinty=tlog3e^sint?