What is the derivative of re^{rx} ?

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

\frac{d}{d x} (4 (5 - 7 x)^{5})

f (x) = \frac{3}{( x + 1 ) ^{2}}

e^{- 5 x^{4}}

\frac{d}{d x} (2^{arcsech (x)})

\int \frac{x}{x ^{4} + 3} d x

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