Scientific Calculator

Partial Derivative Calculator

calculator_partial_derivative

Read-only

Partial derivative of a multivariable expression with respect to a specified variable.

Tool call template

Replace each placeholder with a value matching the input schema. Only required parameters are included; add optional parameters as needed.

{
  "id": 1,
  "jsonrpc": "2.0",
  "method": "tools/call",
  "params": {
    "arguments": {
      "expression": "<expression>",
      "variable": "<variable>"
    },
    "name": "calculator_partial_derivative"
  }
}

Input Schema

Name	Required	Description
`order`	No	Derivative order (default 1).
`variable`	Yes	Variable to differentiate with respect to.
`expression`	Yes	Multivariable expression.

Output Schema

Name	Required	Description	Default
`result`	Yes
`variable`	Yes
`expression`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

First observedOct 23, 2026

TDQS

B3.4/5.0

Behavior3/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

The annotations already establish that this is a read-only, non-destructive, closed-world operation, so the safety profile is covered. The description adds no further behavioral detail beyond the basic computation, but it also does not contradict the annotations.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is a single precise sentence with no filler and the core operation is front-loaded. Every part of the sentence earns its place.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness4/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a simple symbolic calculator with full schema coverage, an output schema, and clear safety annotations, the description states enough to invoke the operation correctly. It is slightly incomplete in not helping distinguish this from related derivative tools, but the structured fields cover the mechanics.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters3/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 100%, so the schema already documents expression, variable, and order with examples and defaults. The description reinforces the expression and variable concepts but does not add meaning beyond the schema, such as for higher-order derivatives via the order parameter.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose4/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly identifies a partial derivative operation on a multivariable expression with respect to a specified variable. The word 'partial' implicitly distinguishes it from ordinary derivative siblings, but it does not explicitly name or contrast those sibling tools.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines2/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

There is no guidance on when to use this tool versus calculator_derivative, calculator_second_derivative, calculator_numerical_derivative, or calculator_gradient. The description states what it does but leaves alternative selection entirely to inference.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

All Scientific Calculator tools Inspect

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