derivative of (5x^3-7/x)

解答

\frac{d}{d x} (\frac{5 x ^{3} - 7}{x})

\frac{10 x ^{3} + 7}{x ^{2}}

求解步骤

\frac{d}{d x} (\frac{5 x ^{3} - 7}{x})

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

\frac{d}{d x} (5 x^{3} - 7) = 15 x^{2}

\frac{d x}{d x} = 1

= \frac{15 x ^{2} x - 1 \cdot ( 5 x ^{3} - 7 )}{x ^{2}}

化简

\frac{15 x ^{2} x - 1 \cdot ( 5 x ^{3} - 7 )}{x ^{2}} : \frac{10 x ^{3} + 7}{x ^{2}}

= \frac{10 x ^{3} + 7}{x ^{2}}

f (x) = 10 cos (30 x - 7)

\int \frac{- 2 x}{1 + x ^{2}} d x

\frac{\partial}{\partial x} (e^{- 8 x})

\frac{d}{d y} (cos (2 y))

x \to 0 - lim (5 x^{3} - 7 x^{2} + 2^{x} - 2)