The same definition is applied to the tangent plane; tangent plane to a surface at a given point is the plane that just touches the surfaces at that point.

Let a function y = f (x) then the Slope of the tangent is the gradient of the function i.e. dy / dx. Then the equation of the tangent line (L, M) is given by:

y – M = dy / dx ( L ) . (x - L)

Where ( x, y) denotes the coordinates of any point on the tangent line. The tangent line’s equation can be determined by the use of polynomial division to divide ∫ f(x) by ( x – L )

^{2}if the remainder is denoted by the function g(x) then the equation of the tangent line is given by:

y = g( x)

When the equation of the curve having two variables and denoted by f(x, y) = 0 then the slope of the function is given by:

dy / dx = - ( δf / δx) / ( δf / δy ),

Then the expression for the tangent function or tangent line is given by:

( δf/ δx ) (L, M). (x - L) + ( δf / δy )(L , M) . ( y - M) = 0.