derivative of sqrt(5x-4y)

解答

\frac{d}{d x} (5 x - 4 y)

\frac{5 - 4 \frac{d y}{d x}}{2 5 x - 4 y}

求解步骤

\frac{d}{d x} (5 x - 4 y)

使用连锁律:

\frac{1}{2 5 x - 4 y} \frac{d}{d x} (5 x - 4 y)

= \frac{1}{2 5 x - 4 y} \frac{d}{d x} (5 x - 4 y)

\frac{d}{d x} (5 x - 4 y) = 5 - 4 \frac{d y}{d x}

= \frac{1}{2 5 x - 4 y} (5 - 4 \frac{d y}{d x})

化简

\frac{1}{2 5 x - 4 y} (5 - 4 \frac{d y}{d x}) : \frac{5 - 4 \frac{d y}{d x}}{2 5 x - 4 y}

= \frac{5 - 4 \frac{d y}{d x}}{2 5 x - 4 y}

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