derivative of sqrt(x*y)

解答

\frac{d}{d x} (x \cdot y)

\frac{y + x \frac{d y}{d x}}{2 x y}

求解步骤

\frac{d}{d x} (x y)

使用连锁律:

\frac{1}{2 x y} \frac{d}{d x} (x y)

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

\frac{d}{d x} (x y) = y + x \frac{d y}{d x}

= \frac{1}{2 x y} (y + x \frac{d y}{d x})

化简

\frac{1}{2 x y} (y + x \frac{d y}{d x}) : \frac{y + x \frac{d y}{d x}}{2 x y}

= \frac{y + x \frac{d y}{d x}}{2 x y}

\int 2 x y^{3} d x

\int x^{2} cos (3 x) d x

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\frac{d}{d x} (ln ((x + 6)^{11}))