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The limit definition of a derivative is the finite real limit of the difference quotient as the nonzero increment tends to zero. At an interior point where this limit exists, it represents the derivative and the tangent slope.

Conditions: A finite real derivative limit must exist at the point.; The point is interior and $Δx\ne 0$ while taking the limit.

The limit definition of a derivative is the finite real limit of the difference quotient as the nonzero increment tends to zero. At an interior point where this limit exists, it represents the derivative and the tangent slope.

Conditions: A finite real derivative limit must exist at the point.; The point is interior and $Δx\ne 0$ while taking the limit.