derivative of-(a^2x/(b^2y))

解答

\frac{d}{d x} (- \frac{a ^{2} x}{b ^{2} y})

- \frac{a ^{2} ( y - x \frac{d y}{d x} )}{b ^{2} y ^{2}}

求解步骤

\frac{d}{d x} (- \frac{a ^{2} x}{b ^{2} y})

将常数提出:

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

= - \frac{a ^{2}}{b ^{2}} \frac{d}{d x} (\frac{x}{y})

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= - \frac{a ^{2}}{b ^{2}} \cdot \frac{\frac{d x}{d x} y - \frac{d y}{d x} x}{y ^{2}}

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

= - \frac{a ^{2}}{b ^{2}} \cdot \frac{1 \cdot y - \frac{d y}{d x} x}{y ^{2}}

化简

- \frac{a ^{2}}{b ^{2}} \cdot \frac{1 \cdot y - \frac{d y}{d x} x}{y ^{2}} : - \frac{a ^{2} ( y - x \frac{d y}{d x} )}{b ^{2} y ^{2}}

= - \frac{a ^{2} ( y - x \frac{d y}{d x} )}{b ^{2} y ^{2}}

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