derivative

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

No annotations are provided, so the description must disclose behavioral traits. It only states the basic calculation and does not mention side effects, input format expectations, output structure, or edge-case behavior. For a pure computational tool, this is a minimal but not transparent description.

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

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

A single concise sentence that immediately states the action and subject, with no extraneous words. It is front-loaded with the verb and is highly efficient.

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

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

With no output schema, the description does not explain what the tool returns (e.g., the derivative expression). It also lacks usage guidance and edge-case handling, making it insufficient for a complete understanding of the tool's behavior.

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

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

The description clarifies the role of 'variable' as the differentiation variable and 'expression' as the operand, adding meaning beyond the bare schema property names, which carry no descriptions. It helps the agent understand how the two parameters relate.

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

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

The description uses the specific verb 'Calculate' and identifies the resource as 'the derivative of an expression with respect to a variable', which clearly differentiates it from the generic sibling 'calculate'. It concisely states exactly what the tool does.

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

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

No guidance is provided about when to use this tool versus the sibling 'calculate'. There is no mention of exclusions, prerequisites, or contexts where differentiation is appropriate, leaving the agent to infer usage.

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