deriveFind the derivative of an expression with respect to x. Input algebraic notation (e.g., "x^2"). Returns the derivative.
| Name | Required | Description | Default |
|---|---|---|---|
| expression | Yes | Expression to differentiate (e.g., "x^2", "sin(x)", "x^3+2x^2+x") |
| Name | Required | Description | Default |
|---|---|---|---|
| input | Yes | The input expression | |
| result | Yes | Derivative expression or null | |
| operation | Yes | Operation name (derive) |
Changes observed during successful MCP inspections.
Output schema / (root)Previous value: -nullNew value: +{
+ "properties": {
+ "input": {
+ "description": "The input expression",
+ "type": "string"
+ },
+ "operation": {
+ "description": "Operation name (derive)",
+ "type": "string"
+ },
+ "result": {
+ "description": "Derivative expression or null",
+ "type": [
+ "string",
+ "null"
+ ]
+ }
+ },
+ "required": [
+ "operation",
+ "input",
+ "result"
+ ],
+ "type": "object"
+}Input schema / examplesAdded value: +[
+ {
+ "expression": "x^2"
+ },
+ {
+ "expression": "x^3+2x^2+x"
+ }
+]Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
Annotations already declare readOnlyHint, idempotentHint, and destructiveHint=false, so safety is established. The description adds that algebraic notation is accepted and the derivative is returned, which is useful but not extensive beyond the annotations.
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 brief and front-loaded, but the final sentence 'Returns the derivative' repeats information from the first sentence, so not every sentence is strictly necessary.
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 single-parameter math tool with an output schema and strong annotations, the description sufficiently specifies input form, variable, and return value. No major context is missing.
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 schema already documents the single parameter with examples, providing 100% coverage. The description adds the key detail that differentiation is with respect to x, which the schema does not state.
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 'Find the derivative of an expression with respect to x,' which identifies the specific operation and resource. It naturally distinguishes itself from sibling tools like factor 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: it is for differentiating an algebraic expression with respect to x. It does not explicitly mention alternatives, but the operation is unambiguous and no exclusions are needed.
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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