(\partial)/(\partial x)(log_{10}(xy))

解答

\frac{\partial}{\partial x} (lo g_{10} (x y))

\frac{1}{ln ( 10 ) x}

求解步骤

\frac{\partial}{\partial x} (lo g_{10} (x y))

将

y

视为常数

使用对数计算法则:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

= \frac{\partial}{\partial x} (\frac{ln ( x y )}{ln ( 10 )})

将常数提出:

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

= \frac{1}{ln ( 10 )} \frac{\partial}{\partial x} (ln (x y))

使用连锁律:

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

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

\frac{\partial}{\partial x} (x y) = y

= \frac{1}{ln ( 10 )} \cdot \frac{1}{x y} y

化简

\frac{1}{ln ( 10 )} \cdot \frac{1}{x y} y : \frac{1}{ln ( 10 ) x}

= \frac{1}{ln ( 10 ) x}

a re a y = x^{2} - 2 x, y = - x^{2} + 4 x

x \to 2 + lim (\frac{3}{x ^{2} - 4})

n = 1 \sum \infty \frac{1}{n ^{4} + 1}

\frac{\partial}{\partial x} (\frac{1}{x + 4 y})

\int 28 t (7 t^{2} - 5)^{3} d t