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In calculus (a branch of mathematics), a differentiable function of one real variable is a function whose derivative exists at each point in its domain.
Part B: Differentiability. Note To understand this topic, you will need to be familiar with limits, as discussed in the chapter on derivatives in Calculus Applied to the Real World. If you like, you can review the topic summary material on derivatives and limits or, for a more detailed study, the on-line tutorial on derivatives. To begin, we recall the definition of the derivative of a function, and what it means for a function to be differentiable.