What is the difference between dy/dx, Δy/Δx, δy/δx and ∂y/∂x?

What is the difference between dy/dx, Δy/Δx, δy/δx and ∂y/∂x?

The symbols are d, upper case delta, lower case delta, and lower case del.

dy/dx : is the gradient of the tangent at a point on the curve y=f(x)

Δy/Δx : is the gradient of a line through two points on the curve y=f(x)

δy/δx is the gradient of the line between two ponts on the curve y=f(x) which are close together

∂y/∂x is the gradient of the tangent through a point on the surface y=f(x,z,...) in the direction of the x axis.

The lower case delta just indicates a small change - not an infinitesimally small change.

It's a short-hand notation whose meaning depends on the context.

You will get a better understanding of the others when you see the more general forms - like the gradient operator, and the relationship to line and surface integrals.

Read more: http://www.physicsforums.com/

For dy, Δy and ∂y i quote ProfRay's answer.

In some physics textbook, the author uses δy to denote the so-called "exact differential", i.e. the differential of a quantity whose path-integral on any curve that joins two points A,B does not depend on the curve, but only on A,B (some kind of quantity that ammits potential). For example is well know in termodynamics that the heat Q have a non-exact differential (heat variation depends on the kind of transformation) but Q/T (where T is the temperature) admits exact differential (entropy).

For reference: http://en.wikipedia.org/wiki/Exact_differential

it's a matter of different hieroglyphics.

no need

dy, Δy, δy are the same.

∂y is for partial derivatives.