derivative (sqrt(25-x^2))/(4x)

解答

导数

\frac{25 - x ^{2}}{4 x}

- \frac{25}{4 x ^{2} 25 - x ^{2}}

求解步骤

\frac{d}{d x} (\frac{25 - x ^{2}}{4 x})

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{4} \frac{d}{d x} (\frac{25 - x ^{2}}{x})

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{1}{4} \cdot \frac{\frac{d}{d x} ( 25 - x ^{2} ) x - \frac{d x}{d x} 25 - x ^{2}}{x ^{2}}

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

\frac{d x}{d x} = 1

= \frac{1}{4} \cdot \frac{( - \frac{x}{25 - x ^{2}} ) x - 1 \cdot 25 - x ^{2}}{x ^{2}}

化简

\frac{1}{4} \cdot \frac{( - \frac{x}{25 - x ^{2}} ) x - 1 \cdot 25 - x ^{2}}{x ^{2}} : - \frac{25}{4 x ^{2} 25 - x ^{2}}

= - \frac{25}{4 x ^{2} 25 - x ^{2}}

a re a 4 x - x^{2}, x^{2}

x \to - 4 lim ((2 x + 3) (x^{2} - 1))

\int e^{2 y^{2}} d y

x \to 4 lim (- x + 7)

n = 1 \sum \infty \frac{2}{1 0 ^{n}}