dy/dt for y = (1+e^t) ln t

find the derivaties and simplify

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`y= (1+e^t) ln t`

We need to find the derivative `(dy)/(dt)`

==> We will use the product rule:

If `y= u*v ==gt y' = u'v + uv` '

`==gt y'= (1+e^t)'(lnt) + (1+e^t)(lnt)'`

`==gt y'= (e^t)(lnt) + (1+e^t)(1/t) `

`==gt y' = (e^t)lnt + 1/t + (e^t)/t`

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