What is the difference between partial derivative (∂) and total derivative (d)?

The total derivative (d/dx) represents rate of change with respect to a single independent variable. The partial derivative (∂/∂x, \partial) measures change with respect to one variable while holding all other variables constant in multivariable functions.

What is the Del / Nabla operator (∇) used for?

The nabla operator (∇, \nabla) is a vector differential operator used in multivariable calculus and physics to compute gradients (∇f), divergence (∇ · F), curl (∇ × F), and Laplacians (∇²f).

Calculus Symbols Hub In Progress (Stub)

Calculus Symbols

Explore our complete math symbols list and interactive keyboard to lookup meanings, LaTeX codes, and UTF-8 characters for calculus symbols. Notations for derivatives, partial derivatives, integrals, limits, gradients, deltas, and infinitesimal differentials.

Calculus Symbols Reference Table

Catalog of Calculus Symbols with LaTeX and Unicode Codes
Symbol	Name	Meaning	Example	LaTeX	Unicode
∫	Integral	Calculates the area under a curve, antiderivative, or continuous accumulation.	∫ 2x dx = x² + C	`\int`	`U+222B`
∬	Double Integral	Integration over a two-dimensional planar region.	∬_R f(x, y) dA	`\iint`	`U+222C`
∭	Triple Integral	Integration over a three-dimensional solid volume.	∭_V f(x, y, z) dV	`\iiint`	`U+222D`
∮	Contour Integral (Closed Loop)	Line integral taken along a closed path or contour in complex analysis / physics.	∮_C F · dr = 0	`\oint`	`U+222E`
∂	Partial Derivative (Del / Curly d)	Derivative of a multivariable function with respect to one variable holding others constant.	∂f/∂x = 2xy	`\partial`	`U+2202`
∇	Nabla / Del (Gradient)	Vector differential operator representing gradient, divergence, or curl.	∇f = (∂f/∂x, ∂f/∂y, ∂f/∂z)	`\nabla`	`U+2207`
lim	Limit	Value that a function or sequence approaches as the input approaches some value.	lim_{x → 0} (sin x)/x = 1	`\lim_{x \to a}`	`U+006C`
d/dx	Derivative Operator	Instantaneous rate of change of a function with respect to variable x.	d/dx (x³) = 3x²	`\frac{d}{dx}`	`U+0064`
f'(x)	Prime Derivative Notation	Lagrange's notation for the first derivative of a function.	f(x) = x² ⟹ f'(x) = 2x	`f'(x)`	`U+2032`
∯	Surface Integral	Closed double integral over a closed 2D boundary surface.	∯_S B · dA = 0	`\oiint`	`U+222F`
⨌	Quadruple Integral	Integral evaluated across a four-dimensional mathematical volume.	⨌_V f(x,y,z,t) dV	`\iiiint`	`U+2A0C`
∰	Volume Integral	Closed triple integral over a 3D closed hypersurface.	∰_V ρ dV = Q	`\oiiint`	`U+2230`