C h a p t e r 3 S e c t i o n 2 {\displaystyle \mathbf {Chapter3Section2} }
d d x [ s i n ( x ) ] = c o s ( x ) d d x [ c s c ( x ) ] = − c s c ( x ) ⋅ c o t ( x ) {\displaystyle {\frac {d}{dx}}[sin(x)]=cos(x)\qquad {\frac {d}{dx}}[csc(x)]=-csc(x)\cdot cot(x)} d d x [ c o s ( x ) ] = − s i n ( x ) d d x [ s e c ( x ) ] = s e c ( x ) ⋅ t a n ( x ) {\displaystyle {\frac {d}{dx}}[cos(x)]=-sin(x)\qquad {\frac {d}{dx}}[sec(x)]=sec(x)\cdot tan(x)} d d x [ t a n ( x ) ] = s e c 2 ( x ) d d x [ c o t ( x ) ] = − c s c 2 ( x ) d r {\displaystyle {\frac {d}{dx}}[tan(x)]=sec^{2}(x)\qquad {\frac {d}{dx}}[cot(x)]=-csc^{2}(x)dr} E x a m p l e s {\displaystyle \mathbf {\color {Blue}{Examples}} } E x .2 {\displaystyle \mathbf {Ex.2} } f ( x ) = s e c ( x ) 1 + t a n ( x ) {\displaystyle f(x)={\frac {sec(x)}{1+tan(x)}}}
![{\displaystyle {\frac {d}{dx}}[cos(x)]=-sin(x)\qquad {\frac {d}{dx}}[sec(x)]=sec(x)\cdot tan(x)}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/3b99fcc29101c0e795846ec067bd0064de5836b5)
![{\displaystyle {\frac {d}{dx}}[sin(x)]=cos(x)\qquad {\frac {d}{dx}}[csc(x)]=-csc(x)\cdot cot(x)}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/8d2f5fc8222b617f8de5a2b46ddf1d9924e652b0)
![{\displaystyle {\frac {d}{dx}}[tan(x)]=sec^{2}(x)\qquad {\frac {d}{dx}}[cot(x)]=-csc^{2}(x)dr}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/956faa87084ddddcf482b7d87019aca4ed074d14)
