turunan fungsi implisit dari tan(xy) – 2y = 0
Posted by andi telaumbanua on Feb 13, 2018 in Matematika |
Tentukan turunan pertama dari bentuk implisit tan(xy)- 2y = 0 !
Jawab :
Turunan bentuk implisit
Pertama kita turunkan dulu tan(xy)
Misalkan : u = xy
maka: du/dx=(1)(y)+ (x)(dy/dx)=y+x dy/dx
Maka: y = tan u
maka: dy/du=sec^2u=sec^2(xy)
Sehingga :
dy/dx =(dy/du)(du/dx)
dy/dx =(sec^2(xy) )(y+x dy/dx)
dy/dx =y sec^2(xy)+ x sec^2(xy) dy/dx
Maka:
(d(tan (xy)- 2y))/dx = (d(0))/dx
d(tan (xy))/dx- d(2y)/dx =0
y sec^2(xy)+ x sec^2(xy) dy/dx
-(d(2y)/dx)(dy/dx) =0
y sec^2(xy)+ x sec^2(xy) dy/dx
-2 dy/dx =0
dy/dx [x sec^2(xy)-2] =-y sec^2(xy)
dy/dx = [-y sec^2(xy)]/[x sec^2(xy) – 2 ]
