Derivatives

In Corca, derivatives can be written in multiple standard notations. All supported forms behave consistently and can be evaluated, modified, or reused.

Creating a derivative

You can create a derivative by typing standard derivative notation. Type derivative. A structured derivative expression appears: d()/d().

Common derivative notations

Multiple derivative styles are supported. They are interpreted automatically.

Using prime notation

Prime notation is available as a postfix operator: f(x)'. Result: (ƒ^′)(x). Prime symbols remain attached to the function and move with it.

Higher-order derivatives

Higher-order derivatives use powers to represent the derivative order: d2(x3)/(d(x)2)

The order is represented structurally as an exponent. This representation avoids ambiguity and keeps the expression consistent.

Partial derivatives

Partial derivatives describe change with respect to one variable in a multivariable function.

∂(x2*y)/∂(x)

Meaning:

Differentiate with respect to x while holding y constant.

Multiple variables are supported:

∂2(ƒ(x,y))/(∂(x)*∂(y))

Writing derivatives with fractions

Fraction-style derivatives are recognized automatically. Type df/dx. Result: a structured derivative expression: d(ƒ)/d(x).

Corca detects derivative patterns and distinguishes them from ordinary division.

If the pattern does not match derivative notation, the expression remains a fraction.

Derivatives inside expressions

Derivatives can appear anywhere in a calculation:

y=d(x2+3*x)/d(x)

Result:

y=d(x2+3*x)/d(x)=3+2*x

The derivative behaves like a standard mathematical object.

Editing derivatives

You can modify any component of a derivative.

Original:

d(x2)/d(x)

Update variable:

d(t2)/d(t)

The function remains unchanged.

Cursor behavior in derivatives

Derivative expressions support predictable navigation.

This makes editing complex formulas more reliable.

Derivatives in imported content

Derivatives imported from LaTeX are converted into structured expressions.

Example input:

\frac{d}{dx} x^2

Result:

A structured derivative expression: d()/d(x)*x2

Imported derivatives behave exactly like native ones.