Mode Visualisasi:
Pahami partial derivatives dengan melihat 2D slices dari fungsi 3D
Partial Derivatives: Dari 2D ke 3D
Sekarang kita memperluas konsep derivatives ke fungsi dengan dua variabel. Alih-alih satu tangent line, kita memiliki dua directional slopes!
Fungsi 3D:
$$f(x, y) = x^2 + y^2 - xy + 1$$
Partial Derivatives:
$$\frac{\partial f}{\partial x} = 2x - y \quad \text{(slope di arah x)}$$ $$\frac{\partial f}{\partial y} = 2y - x \quad \text{(slope di arah y)}$$
$$f(x, y) = x^2 + y^2 - xy + 1$$
Partial Derivatives:
$$\frac{\partial f}{\partial x} = 2x - y \quad \text{(slope di arah x)}$$ $$\frac{\partial f}{\partial y} = 2y - x \quad \text{(slope di arah y)}$$
$\frac{\partial f}{\partial x}$ pada titik saat
ini:
0.0
Rate of change saat bergerak di arah x
0.0
Rate of change saat bergerak di arah x
$\frac{\partial f}{\partial y}$ pada titik saat
ini:
0.0
Rate of change saat bergerak di arah y
0.0
Rate of change saat bergerak di arah y
Gradient Vector:
$$\nabla f = \left(\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}\right) = \left(0.0, 0.0\right)$$
$$\nabla f = \left(\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}\right) = \left(0.0, 0.0\right)$$
Gradient menunjuk ke arah kenaikan paling cepat!