मूल नियमो से `sqrt(sin x)` का अवकल - गुणांक ज्ञात कीजिए ।

Explanation

माना ` f(x) = sqrt( sin x) = y " तो " f( x+h) = sqrt(sin ( x+h))`
` d/(dx) sqrt( sin x) = lim _( h to 0) (sqrt( x+h) - sqrt( sin x))/h`
` = lim _( h to 0) ( sqrt( sin ( x+h)) - sqrt( sin x))/hxx (sqrt(sin(x+h))+sqrt(sin x))/(sqrt(sin(x+h))+sqrt(sin x))`
` = lim _( h to 0 ) (sin ( x+h) - sin x)/(h[sqrtsin(x+h)+sqrt(sin x)])`
` = lim _ ( h to 0) ( 2cos (x + 1/2 h)sin. 1/2h)/(h[sqrt( sin ( x+h))+ sqrt( sin x)])`
` lim _ ( h to 0) ( cos ( x+ 1/2 h))/( sqrt( sin ( x+h))+ sqrt( sinx ))xx lim _( h to 0) ( sin1/2h)/(1/2h)`
` = ( cos x)/( sqrt( sin x)+sqrt( sin x))xx 1 = ( cos x)/( 2 sqrt( sin x))`