((log_{10}(x))/x)^'

解答

(\frac{lo g _{10} ( x )}{x})^{^{'}}

\frac{1 - ln ( x )}{ln ( 10 ) x ^{2}}

求解步骤

(\frac{lo g _{10} ( x )}{x})^{'}

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{( lo g _{10} ( x ) ) ^{^{'}} x - x ^{^{'}} lo g _{10} ( x )}{x ^{2}}

(lo g_{10} (x))^{'} = \frac{1}{x ln ( 10 )}

x^{'} = 1

= \frac{\frac{1}{x l n ( 10 )} x - 1 \cdot lo g _{10} ( x )}{x ^{2}}

化简

\frac{\frac{1}{x l n ( 10 )} x - 1 \cdot lo g _{10} ( x )}{x ^{2}} : \frac{1 - ln ( x )}{ln ( 10 ) x ^{2}}

= \frac{1 - ln ( x )}{ln ( 10 ) x ^{2}}

t an g e n t \frac{6}{5 x + 3}

d er i v a t i v e u (x) = 2 x

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

\frac{\partial}{\partial x} ((2 x)^{x})

\int_{1}^{11} \frac{1}{x - 7} d x