derivative of ((x-sqrt(x))/(x^{1/5)})

解答

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

\frac{3 ( x - 1 )}{10 x ^{\frac{7}{10}}} + \frac{1}{2 x ^{\frac{1}{5}}}

求解步骤

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

化简

\frac{( x - x )}{x ^{\frac{1}{5}}} : x^{\frac{3}{10}} (x - 1)

= \frac{d}{d x} (x^{\frac{3}{10}} (x - 1))

使用微分乘法定则:

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

f = x^{\frac{3}{10}}, g = x - 1

= \frac{d}{d x} (x^{\frac{3}{10}}) (x - 1) + \frac{d}{d x} (x - 1) x^{\frac{3}{10}}

\frac{d}{d x} (x^{\frac{3}{10}}) = \frac{3}{10 x ^{\frac{7}{10}}}

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

= \frac{3}{10 x ^{\frac{7}{10}}} (x - 1) + \frac{1}{2 x ^{\frac{1}{2}}} x^{\frac{3}{10}}

化简

\frac{3}{10 x ^{\frac{7}{10}}} (x - 1) + \frac{1}{2 x ^{\frac{1}{2}}} x^{\frac{3}{10}} : \frac{3 ( x - 1 )}{10 x ^{\frac{7}{10}}} + \frac{1}{2 x ^{\frac{1}{5}}}

= \frac{3 ( x - 1 )}{10 x ^{\frac{7}{10}}} + \frac{1}{2 x ^{\frac{1}{5}}}

d er i v a t i v e 100 - \frac{200}{t ^{2} + 4}

d er i v a t i v e - \frac{5}{x ^{5}}

y^{^{''}} + 25 y = cos (4 t)

n = 1 \sum \infty \frac{( n )}{2 ^{n}}

t an g e n t (x + 2)^{2} + (y - 3)^{2} = 37, (- 1, - 3)