What is (\partial)/(\partial t)(Pe^{rt}) ?

The answer to (\partial)/(\partial t)(Pe^{rt}) is Pe^{rt}r

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(\partial)/(\partial t)(Pe^{rt})

\frac{\partial}{\partial t} (P e^{r t})

P e^{r t} r

Solution steps

\frac{\partial}{\partial t} (P e^{r t})

Treat

P, r

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= P \frac{\partial}{\partial t} (e^{r t})

Apply the chain rule:

e^{r t} \frac{\partial}{\partial t} (r t)

= e^{r t} \frac{\partial}{\partial t} (r t)

\frac{\partial}{\partial t} (r t) = r

= P e^{r t} r

What is (\partial)/(\partial t)(Pe^{rt}) ?
The answer to (\partial)/(\partial t)(Pe^{rt}) is Pe^{rt}r