derivative of (5x^2-3x^5/(-sqrt(x)))

解答

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

- \frac{3 x ( - 3 x ^{3} + 5 )}{2} + 9 x^{\frac{7}{2}}

求解步骤

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

化简

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

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

将常数提出:

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

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

使用微分乘法定则:

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

f = x^{\frac{3}{2}}, g = - 3 x^{3} + 5

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

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

\frac{d}{d x} (- 3 x^{3} + 5) = - 9 x^{2}

= - (\frac{3 x}{2} (- 3 x^{3} + 5) + (- 9 x^{2}) x^{\frac{3}{2}})

化简

- (\frac{3 x}{2} (- 3 x^{3} + 5) + (- 9 x^{2}) x^{\frac{3}{2}}) : - \frac{3 x ( - 3 x ^{3} + 5 )}{2} + 9 x^{\frac{7}{2}}

= - \frac{3 x ( - 3 x ^{3} + 5 )}{2} + 9 x^{\frac{7}{2}}

\int_{- \infty}^{\infty} x d x

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