Question

Matematika
b) F(x) =
Dit : F'(x)

Answer 1

secx + cscx
secx - cscx

1 / sinx = cscx
1 / cosx = secx

= ((1/cosx) + (1/sinx)) / ((1/cosx) - (1/sinx))
= ((sinx + cosx) / sinxcosx) / ((sinx - cosx) / sinxcosx)
= (sinx + cosx) / (sinx - cosx)

u = sinx + cosx
u' = cosx - sinx

v = sinx - cosx
v' = cosx + sinx

f ' (x) = u'v - uv' / v²
= ((cosx - sinx)(sinx - cosx) - (sinx + cosx)(cosx + sinx)) / (sinx - cosx)²
= ((sinxcosx - cos²x - sin²x + sinxcosx) - (sinxcosx + sin²x + cos²x + sinxcosx)) / (sinx - cosx)²
= 2sinxcosx - 2sinxcosx - 2cos²x - 2sin²x / (sinx - cosx)²
= -2cos²x - 2sin²x / (sinx - cosx)²
= -2(cos²x + sin²x) / (sinx - cosx)²
= -2 / (sin²x + cos²x - 2sinxcosx)
= -2 / (1 - (sin(x+x) + sin(x-x))
= -2 / (1 - (sin2x + sin0)
= -2 / (1 - sin2x + 0)
= -2 / (1 - sin2x)