derivative of re^{rx}

解答

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

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

求解步骤

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

使用微分乘法定则:

(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})

d er i v a t i v e f (x) = \frac{3}{( x + 1 ) ^{2}}

ma c l a u r in e^{- 5 x^{4}}

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

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