SYMBOLIC ALGEBRA GUIDE

Symbolic algebra simplification and differentiation

A symbolic tool rewrites expressions using algebraic rules. It is useful for exploration, but domain restrictions and formal proof requirements still matter.

FORMULA

d/dx [f(x) · g(x)] = f′(x)g(x) + f(x)g′(x)

WORKED EXAMPLE

For x² + 2x + 1, a simplifier can retain the polynomial form while an algebraic comparison can check it against (x + 1)² by simplifying their difference.

STEP BY STEP

Choose the operation

Use simplify for algebraic rewriting, differentiate for a symbolic derivative, evaluate for a number, or compare to simplify the difference between two forms.

Declare the variable

When differentiating, state the variable. A formula can look similar but produce a different derivative with respect to x versus y.

Read scope notes

A simplifier result is not automatically a formal proof across every domain. Check denominators, square roots, logarithms, and assumptions separately.