How to use MATLAB derivative function

For the MATLAB derivative function, the gradient function is used to calculate the gradient of a scalar function or a vector function, that is, the first-order partial derivative with respect to each independent variable. The syntax is [dx, dy, dz, ...] = gradient(f, dx, dy, dz, ...), where the input f is a function, dx, dy, dz, etc. are optional step parameters, and the output is Partial derivatives along each independent variable.

MATLAB derivative function

Answer:
In MATLAB, ## The #gradient function is used to calculate the gradient of a scalar or vector function, that is, the first-order partial derivative with respect to each independent variable.

Elaboration:

Grammar:

[dx, dy, dz, ...] = gradient(f, dx, dy, dz, ...)

Input:

• f: Scalar function or vector function requiring derivative
• dx, dy, dz: Optional Parameter, specifying the step size in each dimension (default value is 1)

Output:

• dx , dy, dz: For the gradient component of f, the partial derivative along each independent variable

Usage:

• Scalar function:

  f = @(x, y) x^2 + y^2;
  [d_x, d_y] = gradient(f);

• Vector function:

  f = @(x, y) [x^2 + y^2, x - y];
  [d_x1, d_y1, d_x2, d_y2] = gradient(f);

  Note:

  For scalar functions, the output is a vector representing the gradient.
  • For vector functions, the output is a set of vectors representing the gradient of each component.
  • If you do not specify a step size, MATLAB will use the default step size of 1.
  • gradient The function can only differentiate continuous differentiable functions.

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