यदि सभी ` 0 lt x lt pi` के लिए ` f(x) = (sin x)^(sin x) ` है तो f'(x) ज्ञात कीजिए

Explanation

` :' f(x) = (sin x)^(sinx)`
माना ` y = (sin x ) ^(sin x) `
दोनों पक्षों में log लेने पर, ` log y = sin x log ( sin x)`
` 1/y (dy)/(dx) = log ( sin x) d/(dx) sin x + sin x d/(dx) log (sin x) `
` = log ( sin x) xx cos x + sin x xx 1/sinx d/(dx) sinx `
` = cos x . log ( sin x) +n cos x `
` = y. cos x [ 1 + log ( sin x) ] `
` (dy)/(dx) = y. cos x [ 1 + log ( sin x)]`
` = (sin x)^(sinx) . cos x [ 1+ log ( sin x )].`