DefinitionDerivatives are a natural and logical concept in calculus that describe a function’s change or the function’s variable sensitivity. More precisely, the derivative of f(x) at a particular x is the limit of the difference quotient hf(x+h)−f(x), as h approaches zero in case this limit exists. I think the quote from the Los Angeles County Museum of Art is sufficient to clarify the above question: So today we are going to talk about calculus and its applications in reality because it can sound like its religious lore the power of slop mean -- the power of the derivative method represent things like the slope of tangent lines, rates of change it can represent facts of instantaneous -- Point out the fact of interested velocities and accelerations of objects. Moreover, they are important and otherwise useful in optimization, physics, engineering, and more general modeling at analyzing and predicting a function’s or systems’ behavior. For example, we have f(x) = x^2, so f′(x) = 2x gives the change rate of f for any x.
