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sympy_derivative

Compute symbolic derivatives of mathematical expressions to analyze rates of change and solve calculus problems. Enter an expression and variable to differentiate.

Instructions

Create a Derivative object (unevaluated).

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
exprYesString expression
variableYesVariable to differentiate
orderNoOrder of derivative

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault
resultYes
Behavior2/5

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 mentions the output is 'unevaluated', which hints at symbolic rather than numeric computation, but doesn't explain what that means operationally (e.g., returns a symbolic expression, requires evaluation later). It lacks details on error conditions, performance, or side effects for a tool that creates mathematical objects.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is extremely concise—a single sentence with no wasted words. It's front-loaded with the core action ('Create a Derivative object') and includes a clarifying note ('unevaluated'). Every part of the description earns its place, making it efficient for quick scanning.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness3/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given the tool's mathematical nature, 3 parameters, no annotations, but with an output schema (implied by 'Has output schema: true'), the description is minimally adequate. It states what the tool does but lacks context on why to use it, how it differs from siblings, or what the 'Derivative object' entails. The output schema may cover return values, but the description doesn't provide enough guidance for effective use in a broader SymPy ecosystem.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters3/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

The input schema has 100% description coverage, clearly documenting 'expr', 'variable', and 'order' with defaults and types. The description adds no additional parameter semantics beyond what the schema provides (e.g., no examples of valid expressions or variable formats). With high schema coverage, the baseline score of 3 is appropriate as the schema does the heavy lifting.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose3/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description states the action ('Create a Derivative object') and clarifies it's 'unevaluated', which provides some specificity. However, it doesn't clearly distinguish this from sibling tools like 'sympy_diff' (which likely computes derivatives) or explain what a 'Derivative object' represents in the SymPy context. The purpose is understandable but lacks differentiation from alternatives.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines2/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

No guidance is provided on when to use this tool versus alternatives like 'sympy_diff' or other mathematical operations in the sibling list. The description doesn't mention prerequisites, typical use cases, or exclusions. Without this context, an agent must infer usage from the tool name alone.

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

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