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Scientific Calculator

by ai.saifs
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Second Derivative Calculator

calculator_second_derivative
Read-only

Second-order derivative d²f/dx² of an expression.

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>"
    },
    "name": "calculator_second_derivative"
  }
}

Input Schema

NameRequiredDescriptionDefault
variableNoVariable (default x).x
expressionYesMathematical expression.

Output Schema

NameRequiredDescriptionDefault
resultYes
expressionYes

Schema Changelog

Changes observed during successful MCP inspections.

  1. First observed

TDQS

C2.9/5.0
Behavior2/5

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

Annotations already declare readOnlyHint=true and destructiveHint=false, so the safety profile is covered and the description carries no additional burden there. However, the description adds nothing else: it does not say whether the result is symbolic-exact or numeric, whether unsupported expressions error out, or what form the result takes, which matters given a numerical-derivative sibling exists.

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

Conciseness4/5

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

A single front-loaded phrase with no filler. It is terse rather than padded, though the terseness is part of why usage and behavior are under-specified.

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

Completeness3/5

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

An output schema exists and the parameters are fully documented, so the return-value burden is lifted. The remaining gap is disambiguation from the several other derivative tools in the family, which the description leaves entirely unaddressed.

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%, with both the expression and the defaulted variable documented in the schema itself. The description adds no extra meaning about expression syntax (e.g. whether 'x^4' style input is required), so the baseline 3 applies.

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 names a specific operation and resource: the second-order derivative d²f/dx² of an expression. It is unambiguous as to what is computed, but it never distinguishes itself from nearby siblings such as calculator_derivative, calculator_numerical_derivative, or calculator_partial_derivative.

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 statement of when to reach for this tool rather than the first-derivative, numerical-derivative, or partial-derivative siblings. The agent must infer the choice from the name alone.

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

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