Symbolic Derivative

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

With no annotations provided, the description carries the full burden. It discloses key behaviors: differentiation with respect to a specified variable, treating other symbols as free constants, and simplifying the result. An example concretely illustrates the behavior.

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?

The description is two sentences plus an example, front-loaded with the core purpose. Every sentence adds value: the main definition, the example, and the behavioral note on constants/simplification. No wasted words.

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?

For a simple two-parameter differentiation tool with no output schema and no annotations, the description is remarkably complete. It explains the purpose, gives an example, and discloses edge-case behavior (free constants, simplification). The absence of an output schema is compensated by the illustrative yield.

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 input schema already describes both parameters with 100% coverage, so the baseline is 3. The description adds meaning by explaining the role of the variable ('with respect to') and providing a full example that maps parameters to an input/output pair.

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 clearly states the tool computes symbolic derivatives of a mathematical expression with respect to a variable, with a concrete example. This specific verb+resource pairing differentiates it from sibling tools like evaluate and simplify.

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?

The description provides clear context for when to use the tool—when a derivative is needed—through the example and explanation. It doesn't explicitly mention alternatives or when not to use it, but the purpose is unambiguous.

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