implicit_differentiation

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

No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the operation but does not explain what is returned (e.g., dy/dx expression), any limitations, or how dependent_var and independent_var affect the result.

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 a single concise sentence with no filler. It is front-loaded with the core operation and stays appropriately brief for the tool's complexity.

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 annotations and no output schema, the description is too thin to be fully actionable. An agent understands the operation but not the expected output, the role of the variable parameters, or how this tool differs from closely related siblings.

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 covers 100% of parameters, so the baseline is 3. The description adds the implicit-equation framing but does not enrich the meaning of the parameters beyond what the schema already provides.

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 a specific verb and resource: 'Perform implicit differentiation for equations of the form F(x,y) = 0'. It clearly states the operation and the input context, though it is somewhat close to the tool name.

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 implies when to use the tool by restricting it to implicit equations of the form F(x,y) = 0. However, it does not explicitly compare it to siblings like differentiate_symbolic or differentiate_numerical, so an agent gets no direct guidance on when not to use this tool.

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