Tentukan turunan pertama fungsi-fungsi berikut g(x)=(sinx)/(sinx+cosx)

Halo Mino M :) Jawaban: g'(x) = 1/[sin x + cos x]^2 perhatikan konsep turunan berikut: f(x) = sin x => f'(x) = cos x f(x) = cos x => f'(x) = - sin x f(x) = u/v => f'(x) = [u'v - uv']/v^2 perhatikan juga konsep trigonometri berikut: sin^2 x + cos^2 x = 1 Sehingga turunan pertama fungsi g(x)=(sinx)/(sinx+cosx) adalah... g(x)=(sinx)/(sinx+cosx) misal: u = sin x => u' = cos x v = sin x + cos x => v' = cos x - sin x g(x) = u/v g'(x) = [u'v - uv']/v^2 g'(x) = [(cos x)(sin x + cos x) - (sin x)(cos x - sin x)]/[sin x + cos x]^2 g'(x) = [sin x cos x + cos^2 x - sin x cos x + sin^2 x]/[sin x + cos x]^2 g'(x) = [cos^2 x + sin^2 x]/[sin x + cos x]^2 g'(x) = [sin^2 x + cos^2 x]/[sin x + cos x]^2 g'(x) = 1/[sin x + cos x]^2 Jadi, turunan pertama fungsi g(x)=(sinx)/(sinx+cosx) adalah g'(x) = 1/[sin x + cos x]^2 Terima Kasih