Tentukan persamaan garis singgung dari kurva y³ - xy² + cosxy = 2 di titik (0,1) Jawab pakai cara yak

jawab

y³ - xy² + cos (xy) = 2

m = dy/dx

d(y³)/dx - d(xy²)/dx + d (cos(xy)/dx = d(2)/dx

dy/dx =  [ y(sin(xy) + y] / (-2xy - x sin(xy) + 3y²)
untuk x = 0, y = 1
m = [ 1(sin 0) + 1] / (-2(0)(1) - 0(sin (0)+ 3)
m = 1/3

garis singgung  di (0,1) dan m = 1/3
y - y1 = m (x - x1)
y - 1  = 1/3 ( x  -0)
3(y - 1) = x
3y - 3 = x
x - 3y + 3 = 0

m = Dy / DX
Dy / DX =( y × ( sin ) × ( xy ) + y ) / ( - 2xy - x ( sin ( xy ) + 3y2 )
x => 0
y => 1
m = ( 1 × sin 0 + 1 ) / ( -2.0.1 ) - 0 ( sin . 0 + 3 )
m = 1/( - 1 - 0 . 0 + 3 )
m = 1/3

garis singgung x = 0 y = 1 m = 1/3

y - y1 = m - ( x - X1 )
y - 1 = 1/3 - ( x - 0 )
3. y - 1 = x
x - 3y + 3 = 0