Differentiation

Calculates derivative to enable gradient-based algorithms, sensitivity analysis, or solving differential equations

Machine learning: computing gradients for backpropagation; Scientific computing: evaluating analytical derivatives for optimization algorithms; Financial modeling: assessing sensitivity of pricing formulas to input parameters

Scientific computing libraries (e.g., SymPy, TensorFlow, PyTorch), engineering simulations, finance models

deriv(expression, variable)

deriv(..., ...)

expression: a mathematical expression (string, AST, or numeric function); variable: identifier of variable with respect to which derivative is taken

• simplify()
• expand()
• evaluate()
• gradient()
• autograd

• diff()
• derivative()
• grad()
• ∂/∂x notation

Forgetting to specify variable, applying to non-differentiable expressions, confusing derivative with differential, missing chain rule in manual implementation

integral() (computes antiderivative), limit() (computes limit), gradient() (vector of partial derivatives). Derivative gives scalar rate of change; integral gives area under curve; gradient generalizes to multivariable.

Coming from mathematics: may confuse derivative with difference or delta; coming from languages lacking built-in diff, may attempt to implement numerically incorrectly

• differentiation
• integration
• limit
• gradient

For symbolic differentiation, expression must be a valid symbolic object; for automatic differentiation, requires tracking of operations; performance can degrade with large expression trees; not suitable for black-box functions without source

Enables gradient-based optimization and sensitivity analysis without manual derivative derivation

Derive the change: deriv() gives you the slope

In some libraries, deriv() may return a callable that evaluates derivative at a point

higher_order_deriv(expression, variable, order)