turunan dari y: sin x - cos x / sinx + cos x adalah
Jawaban:
u = sin x - cos x
u' = cos x + sin x
v = sin x + cos x
v' = cos x - sin x
f(x) = (u'v - v'u)/v²
=
[tex] \frac{( \cos \: x \: + \: sin \: x)( \sin \: x \: + \cos \: x) - ( \cos \: x \: - \sin \: x )( \sin \: x - \cos \: x) }{( \sin \: x + \cos \: x)( \sin \: x \: + \cos \: x)} [/tex]
=
[tex] \frac{( \cos \: x \: + \: sin \: x)( \sin \: x \: + \cos \: x) - ( \cos \: x \: - \sin \: x )( \sin \: x - \cos \: x) }{( \sin \: x + \cos \: x)( \sin \: x \: + \cos \: x)} [/tex]
[tex] \frac{1 + 2 \sin(x) \cos(x ) + 1 - 2 \sin(x \cos(x)}{1 + 2 \sin(x) \cos(x) } [/tex]
=
[tex] \frac{2}{1 + 2 \sin(x) \cos(x) } [/tex]
[answer.2.content]
