Tìm \(\frac{{d(\tan x)}}{{d(\cot x)}}\)
Ta có:
d\left( {\tan x} \right) = \left( {\tan x} \right)\prime dx = \frac{1}{{{{\cos }^2}x}}dx\\
d\left( {\cot x} \right) = \left( {\cot x} \right)\prime dx = \frac{{ - 1}}{{{{\sin }^2}x}}dx\\
\Rightarrow \frac{{d\left( {\tan x} \right)}}{{d\left( {\cot x} \right)}} = \frac{1}{{{{\cos }^2}x}}dx:\left( {\frac{{ - 1}}{{{{\sin }^2}x}}dx} \right) = - \frac{{{{\sin }^2}x}}{{{{\cos }^2}x}} = - {\tan ^2}x
\end{array}\)
-- Mod Toán 11