y = x^4 sin (1/x^2)
Posted by andi telaumbanua on Feb 17, 2018 in Matematika |
Tentukan turunan pertama dari y = x^4 sin (1/x^2) !
Jawab:
y = uv maka : y^’= u^’ v+uv^’
Pertama cari dy/dx dari sin (1/x^2)
Maka:
dy/dx = cos (1/x^2) d(1/x^2 )/dx
dy/dx = – 2x/x^4 (cos 1/x^2 )
Kemudian carilah dy/dx dari y = x^4 sin (1/x^2 )
dy/dx = d(x^4)/dx sin (1/x^2 ) + x^4 d(sin(1/x^2 )/dx
dy/dx = 4x^3 sin (1/x^2) + x^4 [- 2x/x^4 (cos 1/x^2 )]
dy/dx = 4x^3 sin (1/x^2 ) – 2x cos 1/x^2
dy/dx = 2x(2x^2 sin (1/x^2 ) – cos (1/x^2 )
