Mode Visualisasi:
Pahami partial derivatives dengan melihat berbagai tampilan fungsi 3D
Fungsi 3D Advanced & Visualisasi Contour
Eksplorasi permukaan matematis kompleks dengan berbagai peaks, valleys, dan saddle points. Pelajari bagaimana contour maps mengungkap struktur tersembunyi dari fungsi 3D!
Fungsi 3D Kompleks:
$$f(x, y) = \sin(x) \cos(y) + 0.5(x^2 + y^2) e^{-0.3(x^2 + y^2)}$$
Partial Derivatives:
$$\frac{\partial f}{\partial x} = \cos(x)\cos(y) + x e^{-0.3(x^2 + y^2)}(1 - 0.3(x^2 + y^2))$$ $$\frac{\partial f}{\partial y} = -\sin(x)\sin(y) + y e^{-0.3(x^2 + y^2)}(1 - 0.3(x^2 + y^2))$$
$$f(x, y) = \sin(x) \cos(y) + 0.5(x^2 + y^2) e^{-0.3(x^2 + y^2)}$$
Partial Derivatives:
$$\frac{\partial f}{\partial x} = \cos(x)\cos(y) + x e^{-0.3(x^2 + y^2)}(1 - 0.3(x^2 + y^2))$$ $$\frac{\partial f}{\partial y} = -\sin(x)\sin(y) + y e^{-0.3(x^2 + y^2)}(1 - 0.3(x^2 + y^2))$$
$\frac{\partial f}{\partial x}$ 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!