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Pengertian turuan parsial 
• Secara matematis : 
Diketahui z = f(x,y) fungsi dengan dua 
variabel independen x dan y. Karena x dan y 
independen maka : 
(i). x berubah-ubah sedangkan y 
tertentu. 
(ii). y berubah-ubah sedangkan x 
tertentu.
i) Turunan parsial terhadap variabel x 
Jika x berubah-ubah dan y tertentu maka z merupakan 
fungsi x, Turunan parsial 
z = f(x,y) terhadap x sbb : 
ii) Turunan parsial terhadap variabel y 
Jika y berubah-ubah dan x tertentu maka z merupakan 
fungsi 
y, Turunan parsial z = f(x,y) terhadap y sbb :
• Secara geometri 
permukaan yang memiliki persamaan 푧 = 
푓 푥, 푦 . Bidang y = 푦0 memotong permukaan 
ini pada kurva bidang QPR 
adalah kemiringan garis singgung

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Kalkulus 3

  • 1. Pengertian turuan parsial • Secara matematis : Diketahui z = f(x,y) fungsi dengan dua variabel independen x dan y. Karena x dan y independen maka : (i). x berubah-ubah sedangkan y tertentu. (ii). y berubah-ubah sedangkan x tertentu.
  • 2. i) Turunan parsial terhadap variabel x Jika x berubah-ubah dan y tertentu maka z merupakan fungsi x, Turunan parsial z = f(x,y) terhadap x sbb : ii) Turunan parsial terhadap variabel y Jika y berubah-ubah dan x tertentu maka z merupakan fungsi y, Turunan parsial z = f(x,y) terhadap y sbb :
  • 3. • Secara geometri permukaan yang memiliki persamaan 푧 = 푓 푥, 푦 . Bidang y = 푦0 memotong permukaan ini pada kurva bidang QPR adalah kemiringan garis singgung