Compute the symbolic rate of change of a mathematical expression with respect to a specified variable. Provide an expression and variable to obtain the differentiated result.
Calculate the derivative of an expression with respect to a variable. Example: derivative('x^2', 'x') returns '2*x'
| Name | Required | Description | Default |
|---|---|---|---|
| variable | Yes | Variable to differentiate with respect to | |
| expression | Yes | Mathematical expression |
Changes observed during successful MCP inspections.
v4.1.3Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, and the description only covers basic functionality. It lacks disclosure of limitations, error handling, or behavior for complex expressions (e.g., multivariate or implicit differentiation).
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 extremely concise: one sentence and an example. Every part is necessary and front-loaded.
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 tool with no output schema, the description provides a basic understanding and example. However, it does not explain return format or behavior for edge cases, leaving some gaps.
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?
Both parameters have schema descriptions. The description adds value with an example showing correct parameter order and usage, clarifying syntax beyond the schema.
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 derivatives of expressions with respect to a variable, and the example reinforces this. It distinguishes from sibling tools like solve or simplify by focusing solely on 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 implies usage through the example but does not explicitly state when to use this tool versus alternatives like evaluate or simplify. No exclusions or context are provided.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.