फलन `cos^(2)x` का x के सापेक्ष प्रथम सिद्धांत से अवकल - गुणांक ज्ञात कीजिए ।

Explanation

माना ` f(x) cos^(2) x " " f( x+h) = cos^(2) (x +h)`
` d/(dx) cos^(2) x lim _( h to 0)( cos^(2)(x+h)-cos^(2)x)/h`
` = lim _( h to 0) (-sin ( x + h +x ).sin ( x+h-x))/h`
` [ :' cos^(2) C -cos^(2) D = - sin ( C +D)sin ( C - D)]`
` = lim _ ( h to 0)(-sin (2x+h).sin h)/h`
` = -[ lim _( h to 0) sin ( 2x +h)].[lim_( h to 0)( sin h)/h]`
` = - sin 2x xx1 " " [ :' lim_( h to 0)(sinh)/h =1]`
` = -sin 2x`