derivative (r^5-4r)e^r

解答

导数

(r^{5} - 4 r) e^{r}

(5 r^{4} - 4) e^{r} + e^{r} (r^{5} - 4 r)

求解步骤

\frac{d}{d r} ((r^{5} - 4 r) e^{r})

使用微分乘法定则:

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

f = r^{5} - 4 r, g = e^{r}

= \frac{d}{d r} (r^{5} - 4 r) e^{r} + \frac{d}{d r} (e^{r}) (r^{5} - 4 r)

\frac{d}{d r} (r^{5} - 4 r) = 5 r^{4} - 4

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

= (5 r^{4} - 4) e^{r} + e^{r} (r^{5} - 4 r)

\frac{d y}{d x} = (y^{2} - 9), y (1) = 4

\int e^{x} cos (\frac{x}{2}) d x

\int \frac{2}{x ^{- 1} + 1} d x

\int \frac{4}{x ^{2} - 4 x + 9} d x

d e g 2 r a d (\frac{x ^{'}}{x})^{^{'}}