Through differential calculus, one can calculate the slope of the tangent line to a curve at a point. the slope or gradient of a line describes its steepness, incline, or grade. A higher slope value indicates a steeper incline.


Difference quotient
Forward difference:  ΔF(P) = F(P + ΔP) - F(P);
Central difference:  δF(P) = F(P + ½ΔP)- F(P - ½ΔP);
Backward difference: ∇F(P) = F(P) - F(P - ΔP).

The function difference divided by the point difference is known as the difference quotient

If ΔP is infinitesimal, then the difference quotient is a derivative, otherwise it is a divided difference

∂  -- Partial Derivative

a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant. ∂ often read as "der", "dow", "die", "partial" or simply "d".
The function f can be reinterpreted as a family of functions of one variable indexed by the other variables: In other words, every value of x defines a function, denoted fx, which is (in case of f(x,y)=fx(y)) a function of one real number.
Total derivative