derivative 1/((1-t^2)^{1/2)}

解答

导数

\frac{1}{( 1 - t ^{2} ) ^{\frac{1}{2}}}

\frac{t}{( 1 - t ^{2} ) ^{\frac{3}{2}}}

求解步骤

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

使用指数法则:

\frac{1}{a} = a^{- 1}

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

使用连锁律:

- \frac{1}{2 ( 1 - t ^{2} ) ^{\frac{3}{2}}} \frac{d}{d t} (1 - t^{2})

= - \frac{1}{2 ( 1 - t ^{2} ) ^{\frac{3}{2}}} \frac{d}{d t} (1 - t^{2})

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

= - \frac{1}{2 ( 1 - t ^{2} ) ^{\frac{3}{2}}} (- 2 t)

化简

- \frac{1}{2 ( 1 - t ^{2} ) ^{\frac{3}{2}}} (- 2 t) : \frac{t}{( 1 - t ^{2} ) ^{\frac{3}{2}}}

= \frac{t}{( 1 - t ^{2} ) ^{\frac{3}{2}}}

t an g e n t f (x) = (\frac{x + 1}{x + 3})^{2}, at x = - 2

\int_{0}^{\infty} \frac{( y e ^{- \frac{y}{a}} )}{a} d y

a re a y = x^{2} - 4 x, y = 2 x + 7

\int 3 ln (x^{2} - x + 4) d x

((x - 2)^{2} (x + 4))^{^{'}}