What is the derivative of e^{rx}r ?

The derivative of e^{rx}r is e^{rx}(x(dr)/(dx)+r)r+(dr)/(dx)e^{rx}

What is the first derivative of e^{rx}r ?

The first derivative of e^{rx}r is e^{rx}(x(dr)/(dx)+r)r+(dr)/(dx)e^{rx}

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\frac{d}{d x} (e^{r (x) x} r (x))

e^{r x} (x \frac{d r}{d x} + r) r + \frac{d r}{d x} e^{r x}

Solution steps

\frac{d}{d x} (e^{r x} r)

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{r x}, g = r

= \frac{d}{d x} (e^{r x}) r + \frac{d r}{d x} e^{r x}

\frac{d}{d x} (e^{r x}) = e^{r x} (x \frac{d r}{d x} + r)

= e^{r x} (x \frac{d r}{d x} + r) r + \frac{d r}{d x} e^{r x}

What is the derivative of e^{rx}r ?
The derivative of e^{rx}r is e^{rx}(x(dr)/(dx)+r)r+(dr)/(dx)e^{rx}
What is the first derivative of e^{rx}r ?
The first derivative of e^{rx}r is e^{rx}(x(dr)/(dx)+r)r+(dr)/(dx)e^{rx}