Turunan dari fungsi: A.Y=sin(x²+2) B.Y²+sin(xy)+x²=1

jawab

1) y =  sin (x² +2)
u = x² + 2
du dx = 2x

y = sin u
dy/du = cos u

y' = dy/du. du/dx
y' = sin u . 2x
y'  = 2x sin (x² +2)

2)
y² + sin (xy) + x² = 1
2yy' + (y + xy') cos (xy) + 2x = 0
2yy' + y cos (xy) + xy' cos (xy) + 2x = 0
2yy' + xy' cos (xy) = - 2x - y cos (xy)
y' (2y + x cos (xy)) = -2x - y cos(xy)

y' = { -2x - y cos(xy)) / (2y + x cos (xy))}