derivative of log_{2}(x^2-9x)

解答

\frac{d}{d x} (lo g_{2} (x^{2} - 9 x))

\frac{2 x - 9}{ln ( 2 ) ( x ^{2} - 9 x )}

求解步骤

\frac{d}{d x} (lo g_{2} (x^{2} - 9 x))

使用对数计算法则:

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

= \frac{d}{d x} (\frac{ln ( x ^{2} - 9 x )}{ln ( 2 )})

将常数提出:

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

= \frac{1}{ln ( 2 )} \frac{d}{d x} (ln (x^{2} - 9 x))

使用连锁律:

\frac{1}{x ^{2} - 9 x} \frac{d}{d x} (x^{2} - 9 x)

= \frac{1}{x ^{2} - 9 x} \frac{d}{d x} (x^{2} - 9 x)

\frac{d}{d x} (x^{2} - 9 x) = 2 x - 9

= \frac{1}{ln ( 2 )} \cdot \frac{1}{x ^{2} - 9 x} (2 x - 9)

化简

\frac{1}{ln ( 2 )} \cdot \frac{1}{x ^{2} - 9 x} (2 x - 9) : \frac{2 x - 9}{ln ( 2 ) ( x ^{2} - 9 x )}

= \frac{2 x - 9}{ln ( 2 ) ( x ^{2} - 9 x )}

\frac{d}{d x} ((x^{2} - 1) (x^{2} - 4) (x^{2} - 9))

\frac{\partial}{\partial x} (50 - (4 x^{2} + y^{2}))

\frac{d}{d x} (1 - cos (x))

y^{'} = 0.0013 y (3000 - y)

t an g e n t y = 3 x^{3} - x^{2} + 7, (2, 27)