Dont forget that the little prime mark means 'the derivative of'. Discovered by Gottfried Wilhelm Leibniz and.
The premise is as follows: If two differentiable functions, f (x) and g (x), exist, then their quotient is also differentiable (i.e., the derivative of the quotient of these two functions also exists).
Unless otherwise stated, all functions are functions of real numbers ( R) that return real values although more generally, the formulae below apply wherever they are well defined - including the case of complex numbers ( C).\]īy using the continuity of \(g(x)\), the definition of the derivatives of \(f(x)\) and \(g(x)\), and applying the limit laws, we arrive at the product rule,įormula One car races can be very exciting to watch and attract a lot of spectators. In the first section of this chapter we saw the definition of the derivative and we computed a couple of derivatives using the definition. Other articles will discuss the power rule, chain rule, product rule and quotient rule in more depth. The quotient rule is a method for differentiating problems where one function is divided by another. In order to differentiate more types of functions, 2 new rules will be introduced, the first to enable differentiation of a product of functions, the second to differentiate a quotient. Differential Calculus CHAPTER 19 625 To differentiate such expressions we use the product rule, which can be written as: (a) Let.
#DIFFERENTIAL CALCULUS PRODUCT RULE PLUS#
This is a summary of differentiation rules, that is, rules for computing the derivative of a function in calculus.Įlementary rules of differentiation The Product Rule If f and g are both differentiable, then: which can also be expressed as: The Product Rule in Words The Product Rule says that the derivative of a product of two functions is the first function times the derivative of the second function plus the second function times the derivative of the first function. Product and Quotient Rules The sum, difference and chain rules for differentiating functions are assumed in this course.
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