What is (\partial)/(\partial r)(e^rcos(t)) ?

The answer to (\partial)/(\partial r)(e^rcos(t)) is cos(t)e^r

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(\partial)/(\partial r)(e^rcos(t))

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

cos (t) e^{r}

Solution steps

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

Treat

t

as a constant

Take the constant out:

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

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

Apply the common derivative:

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

= cos (t) e^{r}

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What is (\partial)/(\partial r)(e^rcos(t)) ?
The answer to (\partial)/(\partial r)(e^rcos(t)) is cos(t)e^r