derivative of 1/((25-x^2))

解答

\frac{d}{d x} (\frac{1}{( 25 - x ^{2} )})

\frac{2 x}{( 25 - x ^{2} ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{1}{( 25 - x ^{2} )})

使用指数法则:

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

= \frac{d}{d x} ((25 - x^{2})^{- 1})

使用连锁律:

- \frac{1}{( 25 - x ^{2} ) ^{2}} \frac{d}{d x} (25 - x^{2})

= - \frac{1}{( 25 - x ^{2} ) ^{2}} \frac{d}{d x} (25 - x^{2})

\frac{d}{d x} (25 - x^{2}) = - 2 x

= - \frac{1}{( 25 - x ^{2} ) ^{2}} (- 2 x)

化简

- \frac{1}{( 25 - x ^{2} ) ^{2}} (- 2 x) : \frac{2 x}{( 25 - x ^{2} ) ^{2}}

= \frac{2 x}{( 25 - x ^{2} ) ^{2}}

\int e^{7} d x

y^{^{''}} - 2 y^{^{'}} - 3 y = 3 t e^{2 t}, y (0) = 1, y^{^{'}} (0) = 0

y^{^{'}} = 8 x + y, y (0) = 1

\frac{d y}{d x} = \frac{2 x y - y ^{2}}{x ^{2}}

\frac{d y}{d x} = \frac{4 x ^{3}}{cos ( y )}