partial_derivatives

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 only says 'Compute partial derivatives' and does not explain what is returned, whether it outputs expressions, how mixed/higher-order derivatives are handled, or any limitations. This leaves key behavior unspecified for an agent.

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 front-loaded sentence with no filler. It is appropriately brief, though it could have included a little more operational context without becoming verbose.

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?

There is no output schema and no annotations, so the description needs to explain return behavior and usage context more fully. It does neither, and it leaves the agent without enough information to distinguish this tool from siblings or to understand how mixed_order affects the result.

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 the schema already documents all three parameters. The description does not add extra meaning or clarify the relationship between variables, expression, and mixed_order beyond what the schema provides, so the baseline score of 3 applies.

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 states a clear verb ('Compute') and a specific resource ('partial derivatives for multivariable functions'). It conveys the core operation but does not explicitly distinguish itself from sibling tools such as differentiate_symbolic or gradient_vector, so it stops short of full sibling differentiation.

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 gives no guidance on when to use this tool versus alternatives like differentiate_symbolic, differentiate_numerical, or gradient_vector. It neither names exclusions nor provides context for choosing between partial_derivatives and related symbolic/numerical differentiation tools.

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