derivative of 2ln(xy)

解答

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

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

求解步骤

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

将常数提出:

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

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

使用连锁律:

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

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

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

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

化简

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

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

\int - x^{0} d x

in v erse l a pl a ce \frac{0.2}{( 10 s ^{3} + s ^{2} )}

\int (tan (x) sec^{2} (x)) d x

l a pl a ce t r an s f or m sin (\frac{1}{2} t) \cdot t^{2}

\int - cos (x) 2 x d x