d/(d{r)}({r}sqrt(1-{r)^2})

解答

\frac{d}{d r} (r 1 - r^{2})

1 - r^{2} - \frac{r ^{2}}{1 - r ^{2}}

求解步骤

\frac{d}{d r} (r 1 - r^{2})

使用微分乘法定则:

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

f = r, g = 1 - r^{2}

= \frac{d}{d r} (r) 1 - r^{2} + \frac{d}{d r} (1 - r^{2}) r

\frac{d}{d r} (r) = 1

\frac{d}{d r} (1 - r^{2}) = - \frac{r}{1 - r ^{2}}

= 1 \cdot 1 - r^{2} + (- \frac{r}{1 - r ^{2}}) r

化简

1 \cdot 1 - r^{2} + (- \frac{r}{1 - r ^{2}}) r : 1 - r^{2} - \frac{r ^{2}}{1 - r ^{2}}

= 1 - r^{2} - \frac{r ^{2}}{1 - r ^{2}}

\int \frac{y + 1}{y ^{2} + y + 1} d y

\frac{\partial}{\partial z} (x cos (y) sin (z))

d er i v a t i v e arcsec (5 x)

\frac{\partial}{\partial L} (L^{\frac{1}{4}} K^{\frac{1}{4}})

a re a e^{(\frac{x}{4})}, x = 4, y = 1