Question

Turunan pertama dari g(x) = sin x - cos x per sin x + cos x adalah g ' ( x ) = ...

Answer 1

Misal u = sin x - cos x mka u aksen = -cos x - sin x misal juga v = sin x + cos x mka v aksen = -cos x + sin x sehingga g aksen (x) = (u aksen.v - u.v aksen)/v kuadrat sehingga (-cos x - sin x)(sin x + cos x) - (sin x - cos x)(-cos x + sin x)/
(Sin x + cos x)^ maka g aksen x = - sin x cos x - cos^x - sin^x - sin x cos x + sin x cos x - sin^x - cos^x + sin x cos x/ (sin x + cos x)^ = -2 cos^x - 2 sin^x/ (sin x + cos x)^ mudh2an bermanfaat klw gk salah

Answer 2

U = sinx - cosx
U' = cosx + sinx

V = sinx + cosx
V' = cosx - sinx

g ' (x) = u'v - uv' / v²

= (cosx + sinx)(sinx + cosx) - (sinx - cosx)(cosx - sinx) / (sinx + cosx)²
= (cosx sinx + cos²x + sin²x + cosxsinx) - (cosxsinx - sin²x - cos²x + cosxsinx) / (sinx + cosx)(sinx + cosx)

= ( cos²x + sin²x + 2cosxsinx) - ( - cos²x - sin²x + 2cosxsinx) / (sin²x + cosxsinx + cosxsinx + cos²x)

= cos²x + sin²x + 2cosxsinx + cos²x + sin²x - 2cosxsinx / cos²x + sin²x + 2cosxsinx

= cos²x + sin²x + cos²x + sin²x / cos²x + sin²x + 2cosxsinx
= 1 + 1 / 1 + (sin(x+x) - sin(x-x))
= 2 / 1 + sin2x - sin0
= 2 / 1 + sin2x