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人気のある微分積分 >

(\partial)/(\partial x)(x^{-1/2})

解

\frac{\partial}{\partial x} (x^{- \frac{1}{2}})

解

- \frac{1}{2 x ^{\frac{3}{2}}}

解答ステップ

\frac{\partial}{\partial x} (x^{- \frac{1}{2}})

乗の法則を適用:

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

= - \frac{1}{2} x^{- \frac{1}{2} - 1}

簡素化

- \frac{1}{2} x^{- \frac{1}{2} - 1} : - \frac{1}{2 x ^{\frac{3}{2}}}

= - \frac{1}{2 x ^{\frac{3}{2}}}

人気の例

integral of 5/(sqrt(x^2+2x+5))

\int \frac{5}{x ^{2} + 2 x + 5} d x

tangent f(x)=9+cot(x)-2csc(x),\at x=1

t an g e n t f (x) = 9 + cot (x) - 2 csc (x), at x = 1

limit as t approaches 4 of t|t-4|

t \to 4 lim (t ∣ t - 4 ∣)

limit as x approaches 0 of x pi/2

x \to 0 lim (x \frac{π}{2})

derivative (2x)/(sqrt(x)-1)

d er i v a t i v e \frac{2 x}{x - 1}