derivative of log_{10}(1/x)

解答

\frac{d}{d x} (lo g_{10} (\frac{1}{x}))

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

求解步骤

\frac{d}{d x} (lo g_{10} (\frac{1}{x}))

化简

lo g_{10} (\frac{1}{x}) : - lo g_{10} (x)

= \frac{d}{d x} (- lo g_{10} (x))

将常数提出:

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

= - \frac{d}{d x} (lo g_{10} (x))

使用对数求导法则:

\frac{d}{d x} (lo g_{a} (x)) = \frac{1}{x ln ( a )}

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

y^{^{''}} - 6 y^{^{'}} = 4 x

\int \frac{24}{( 399 x - 1 ) ( 399 + 1 )} d x

\frac{d}{d x} (3 x^{2} + 2 x y - y^{2})

d er i v a t i v e f (x) = (3 - x)^{4} (x + 5)^{3}

\frac{d y}{d t} = y \cdot ln (y)