derivative f(x)=(x+5)/(x-5)

解答

导数

f (x) = \frac{x + 5}{x - 5}

- \frac{10}{( x - 5 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{x + 5}{x - 5})

使用微分除法定则:

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

= \frac{\frac{d}{d x} ( x + 5 ) ( x - 5 ) - \frac{d}{d x} ( x - 5 ) ( x + 5 )}{( x - 5 ) ^{2}}

\frac{d}{d x} (x + 5) = 1

\frac{d}{d x} (x - 5) = 1

= \frac{1 \cdot ( x - 5 ) - 1 \cdot ( x + 5 )}{( x - 5 ) ^{2}}

化简

\frac{1 \cdot ( x - 5 ) - 1 \cdot ( x + 5 )}{( x - 5 ) ^{2}} : - \frac{10}{( x - 5 ) ^{2}}

= - \frac{10}{( x - 5 ) ^{2}}

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

a re a y = cos (x), y = 0.5, 0 \leq x \leq π

1296 y^{^{''}} + 1368 y^{^{'}} + 361 y = 0

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

\int sin^{2} (π x) cos^{5} (π x) d x