निम्न के अवकलन का परिकलन कीजिए :
(i) `f(x) sin 2x` (ii) ` g(x) = ( x+ cos x)/(tanx) ` (iii) `f(x) = ( x^(5) - cos x)/( sinx) `

Explanation

` :' f(x) = sin 2x = 2 sin x cos x `
` :. f'(x) = (d f(x))/(dx) = 2 d/(dx) sin x cos x `
` = 2 [ sin x d/(dx) cos x + cos d/(dx) sin x]`
` = 2 [sin x ( -sin x ) + cos . cos x]`
` = 2 ( - sin^(2) x + cos^(2)x)`
` = 2 ( cos ^(2) x - sin ^(2)x)`
(ii) ` g(x) = ( x+ cos x)/(tanx)`
` g' (x) = ( tanx. d/(dx) ( x+ cos x) - ( x+ cos ) d/(dx) tan x)/( (tan x)^(2))`
` = ( tanx( 1- sin x) - ( x+ cos x) sec^(2) x )/( tan^(2) x)`
` f(x) = ( x^(5) - cos x)/( sin x) `
` f'(x) = ( sin xd/(dx) ( x^(5) - cos x) - ( x^(5) - cos x) d/(dx) sin x)/( sin x)^(2)`
` = ( sin x( 5x^(4) + sin x) - ( x^(5) - cos x) ( cos x))/( sin^(2)x)`
` = ( 5x^(4) sin x + sin^(2) x - x^(5) cos x + cos^(2) x )/( sin^(2)x)`
` = (5x^(4) sin x- x^(5) cos x + 1 )/( sin ^(2)x)`