Partial derivative
A partial derivative is the derivative of a multivariable function with respect to one variable while holding the other variables constant.
Geometry for Programmers
A partial derivative is the derivative of a multivariable function with respect to one variable while the other variables are held constant.
- How it is used
- Guides contour fitting and smooth cubic reconstruction from signed-distance fields and interpolated images.
- How deep it goes
- Defines separate differentiation by coordinate, then uses derivative values in gradients, tangent equations, and continuity extensions.
- Examples
- Uses a two-variable polynomial, SDF contour vertices, cubic segment equations, and raster-image vectorization.
- What you can do after
- Apply it via SymPy and derivative-based equations to construct and stabilize smooth contour segments.
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Advanced Algorithms and Data Structures
A partial derivative is the derivative of a multivariable function with respect to one coordinate while the other coordinates are held constant.
- How it is used
- Deploys partial derivatives as coordinate-wise signals for gradient descent and cost-based optimization.
- How deep it goes
- Explains gradients, update steps, stopping criteria, and numerical alternatives, but does not develop derivative formulas in detail.
- Examples
- Uses two-variable cost surfaces, marble-like downhill motion, force-directed graph embedding, and linear regression parameters.
- What you can do after
- Apply it via gradient descent to update multivariable model parameters or other optimization coordinates.
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Math and Architectures of Deep Learning
The derivative of a multivariable function with respect to one variable while holding the others constant, here squared and accumulated by AdaGrad.
- How it is used
- Explains how individual parameter changes contribute to loss variation in multivariable optimization.
- How deep it goes
- Defines coordinate-wise change, gives a quadratic example, and connects partial derivatives to total change and gradient direction.
- Examples
- Uses L(w0, w1) = 2w0² + 3w1², point P = (3, 4), and line-and-parabola geometry.
- What you can do after
- Evaluate how parameter-wise changes combine and identify the direction that locally decreases loss most.
Read how Math and Architectures of Deep Learning explains partial derivative →
Related concepts
- gradient descentused by · Gradient descent is an iterative optimization method that updates parameters opposite the gradient of an objective function to reduce its value.
- momentumequivalent to · Momentum is an optimization technique that incorporates a running history of gradients or parameter updates to smooth and accelerate movement during training.
- gradientequivalent to · A gradient is the vector of partial derivatives of a scalar function with respect to its variables, indicating its local rate and direction of change.
- tangent vectorproduces · A tangent vector is a vector of first-order derivative values representing sensitivity or instantaneous direction under an input perturbation.
- derivativekind of · A derivative is a mathematical quantity that measures the instantaneous rate of change of a function with respect to an input variable.
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