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

Annotations already declare readOnlyHint=true, destructiveHint=false and openWorldHint=false, so safety is fully covered. The description adds only the default variable behavior; notably it never says the result is symbolic/exact rather than numeric, which is the single most important behavioral difference from calculator_numerical_derivative.

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 efficient sentence with the core operation front-loaded and no filler. It is slightly under-specified rather than over-verbose, which is the better failure mode here.

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 an output schema present and full parameter documentation, the definition is callable as-is. What remains missing is the symbolic-vs-numeric positioning against three closely related siblings, which matters for correct tool selection in this dense calculator family.

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?

Schema description coverage is 100%, so both parameters are already documented in the schema, including the default of x and an expression example. The description restates the default rather than adding syntax conventions (e.g. accepted operators, implicit multiplication) that would genuinely help.

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?

States a specific verb (compute first derivative), the resource (an expression), and the differentiation variable with its default. 'First' implicitly separates it from second_derivative and partial_derivative, but no sibling is named explicitly, so an agent must infer the distinction from the name alone.

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?

There is no guidance on when to choose this over calculator_numerical_derivative, calculator_second_derivative, or calculator_partial_derivative, all present in the sibling list. No exclusions, no prerequisites, no stated input format expectations beyond the schema example.

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