derivative of (((0.06x^2+17x+340))/x)

解答

\frac{d}{d x} (\frac{( ( 0.06 x ^{2} ) + 17 x + 340 )}{x})

\frac{0.06 x ^{2} - 340}{x ^{2}}

求解步骤

\frac{d}{d x} (\frac{( ( 0.06 x ^{2} ) + 17 x + 340 )}{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} ( 0.06 x ^{2} + 17 x + 340 ) x - \frac{d x}{d x} ( 0.06 x ^{2} + 17 x + 340 )}{x ^{2}}

\frac{d}{d x} (0.06 x^{2} + 17 x + 340) = 0.12 x + 17

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

= \frac{( 0.12 x + 17 ) x - 1 \cdot ( 0.06 x ^{2} + 17 x + 340 )}{x ^{2}}

化简

\frac{( 0.12 x + 17 ) x - 1 \cdot ( 0.06 x ^{2} + 17 x + 340 )}{x ^{2}} : \frac{0.06 x ^{2} - 340}{x ^{2}}

= \frac{0.06 x ^{2} - 340}{x ^{2}}

l a pl a ce t r an s f or m 2 e^{\frac{t}{2}}

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t an g e n t f (x) = \frac{2 x}{x ^{2} - 7}, (3, 3)