derivative f(x)=(5x^{3/2}-15^{1/2})/2

解答

导数

f (x) = \frac{5 x ^{\frac{3}{2}} - 1 5 ^{\frac{1}{2}}}{2}

\frac{15 x ^{\frac{1}{2}}}{4}

求解步骤

\frac{d}{d x} (\frac{5 x ^{\frac{3}{2}} - 1 5 ^{\frac{1}{2}}}{2})

将常数提出:

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

= \frac{1}{2} \frac{d}{d x} (5 x^{\frac{3}{2}} - 1 5^{\frac{1}{2}})

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{1}{2} (\frac{d}{d x} (5 x^{\frac{3}{2}}) - \frac{d}{d x} (1 5^{\frac{1}{2}}))

\frac{d}{d x} (5 x^{\frac{3}{2}}) = \frac{15 x ^{\frac{1}{2}}}{2}

\frac{d}{d x} (1 5^{\frac{1}{2}}) = 0

= \frac{1}{2} (\frac{15 x ^{\frac{1}{2}}}{2} - 0)

化简

\frac{1}{2} (\frac{15 x ^{\frac{1}{2}}}{2} - 0) : \frac{15 x ^{\frac{1}{2}}}{4}

= \frac{15 x ^{\frac{1}{2}}}{4}

\int_{- 5}^{5} 25 - x^{2} d x

\frac{d}{d x} ((\frac{1}{x ^{2}} - \frac{3}{x ^{4}}) \cdot (x + 5 x^{3}))

\frac{d}{d x} (a (e^{- 5 x} - 5 e^{- 5 x} x))

\frac{d ^{2}}{d x ^{2}} (x + 1)

d er i v a t i v e \frac{x}{ln ( x )}