**Slope**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.

**Gradient **

**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 Derivativea 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

*f*_{x}, which is (in case of f(x,y)=

*f*_{x}(y)) a function of one real number.

**Total derivative**