What is the derivative of e^{rx} ?

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

- x^{2}

(1 + x^{2})^{2}

e^{2 t} \cdot e^{- 2 t}

\frac{2 ^{n}}{3 ^{n}}

e^{- 6 l n (x)}

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