What is the derivative of e^{rx} ?

The derivative of e^{rx} is e^{rx}x

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

The first derivative of e^{rx} is e^{rx}x

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derivative of

e^{r x}

e^{r x} x

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

= e^{r x} x

\frac{d}{d x} (- e^{- x} x^{2} + 6 e^{- x} x - 6 e^{- x})

\int cot^{3} (10 x) d x

2 \frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + y = 1

\frac{d}{d x} (cos (x^{3} + 2 x))

3 x^{\frac{4}{3}} - 2 x^{\frac{1}{7}}

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