polyder — Differentiate polynomials in MATLAB and RunMat.

polyder differentiates polynomials represented by coefficient vectors. Single-input, product-rule, and rational-function forms follow MATLAB coefficient conventions and output semantics.

Syntax

d = polyder(p)
d = polyder(a, b)
[num, den] = polyder(u, v)

Inputs

Returns

Returned values from polyder depend on how many outputs the caller requests.

Errors

How polyder works

• Accepts real or complex scalars, row vectors, column vectors, or empty vectors. Inputs with more than one non-singleton dimension raise MATLAB-compatible errors.
• Logical and integer coefficients are promoted to double precision before differentiation.
• Leading zeros are removed in outputs (unless the polynomial is identically zero, in which case a single zero coefficient is returned).
• The orientation of the first input polynomial is preserved for the derivative of a single polynomial or a product; the denominator in the quotient rule preserves the orientation of v.
• Calling polyder(p, a) with a single output applies the product rule. Capturing two outputs alongside two input polynomials returns the quotient-rule numerator and denominator (u' * v - u * v', v * v).
• Empty inputs are treated as the zero polynomial.
• When inputs live on the GPU (e.g., gpuArray) and the active provider exposes the polyder hooks, differentiation runs entirely on-device and returns trimmed GPU tensors. Providers that lack the hooks fall back to gathering coefficients to the host, executing the reference CPU implementation, and returning host-resident results. Explicit calls to gpuArray remain available if you need to force residency.

Does RunMat run polyder on the GPU?

When a provider advertises the polyder hooks (the in-process and WGPU backends both do), single polynomials and the product/quotient forms execute fully on the GPU. Outputs preserve the orientation of the leading input while trimming leading zeros exactly as the CPU path does. If the provider declines the request—because the coefficients are complex or the backend lacks support— RunMat automatically gathers the inputs and falls back to the CPU reference implementation to preserve MATLAB compatibility.

Examples

Differentiating a cubic polynomial

p = [3 -2 5 7];   % 3x^3 - 2x^2 + 5x + 7
dp = polyder(p)

Expected output:

dp = [9 -4 5]

Applying the product rule

p = [1 0 -2];    % x^2 - 2
a = [1 1];       % x + 1
dp = polyder(p, a);   % derivative of conv(p, a)

Expected output:

dp = [3 2 -2]

Differentiating a rational function

u = [1 0 -4];      % x^2 - 4
v = [1 -1];        % x - 1
[num, den] = polyder(u, v);    % derivative of (u / v)

Expected output:

num = [1 -2 4];
den = [1 -2 1]

Preserving column-vector orientation

p = [1; 0; -3];    % column vector coefficients
dp = polyder(p)

Expected output:

dp =
     2
     0

Differentiating complex-valued coefficients

p = [1+2i, -3, 4i];
dp = polyder(p)

Expected output:

dp = [2+4i, -3]

Working with gpuArray inputs

g = gpuArray([2 0 -5 4]);
dp = polyder(g);         % stays on the GPU when provider hooks are available
result = gather(dp)

Expected output:

result = [6 0 -5]

Using polyder with coding agents

Open a RunMat example with live inputs, then ask the agent to explain how polyder changes the result.

FAQ

Related Math functions

Open-source implementation

Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how polyder is executed, line by line, in Rust.

• View the source for polyder in Rust on GitHub
• Learn how the RunMat runtime works
• Found a bug? Open an issue with a minimal reproduction.

About RunMat

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