यदि ` y=log sin x +tan x` तब `(dy)/(dx) ` का मान ज्ञात कीजिए| यदि ` x=(pi)/(3)*`

Explanation

` " " y= logsin x+ tan x `
` therefore " "(dy)/(dx) =(d) /(dx) log sin x +(d) /(dx) tan x `
माना ` sin x =t`
` therefore " "(dy)/(dx) =(d)/(dt) log t (d)/(dx) sin x +sec ^(2) x= (1)/(t) cos x+sec ^(2) x `
` " "= (cos x ) /(sinx ) +sec ^(2) x = cot x +sec ^(2)x `
` therefore " "((dy)/(dx) ) _((x=pi //3))=cot ""(pi)/(3)+sec ^(2)"" (pi)/(3) `
` " "= (1)/(sqrt( 3))+ 4 =4 +(1)/(sqrt(3)) `