Calculus Rules: L'Hopital's, Chain, Product, Quotient, Implicit Diff., Quizzes of Mathematics

Download Calculus Rules: L'Hopital's, Chain, Product, Quotient, Implicit Diff. and more Quizzes Mathematics in PDF only on Docsity! TERM 1 L'Hpital's rule DEFINITION 1 Definition TERM 2 Chain Rule DEFINITION 2 d/dx f(g(x)) = f '(g(x)) * g'(x) TERM 3 Product Rule DEFINITION 3 In calculus, the product rule is a formula used to find the derivatives of products of two or more functions. d/dx f(x)g(x)=f '(x)g(x)+f(x)g'(x) TERM 4 Quotient Rule DEFINITION 4 In calculus, the quotient rule is a method of finding the derivative of a function that is the quotient of two other functions for which derivatives exist. d/dx f(x)/g(x) = [f '(x)g(x)-f(x)g'(x)] / [g(x)^2] TERM 5 implicit differentiation DEFINITION 5 In mathematics, an implicit function is a function in which the dependent variable has not been given "explicitly" in terms of the independent variable. y'(x) = dy/dx1.) differentiate both sides w.r.t. "x", writting "y" as "y(x)" using chain rule2.) solve for "y'(x)"3.) plug in "y" and "x" values TERM 6 What rule should be used to solve d/dx f(x)g(x)? DEFINITION 6 Product Ruled/dx f(x)g(x)= f '(x)g(x)+f(x)g'(x) TERM 7 What rule should be used to solve d/dx f(x)/g(x)? DEFINITION 7 quotient rule d/dx f(x)/g(x) = [f '(x)g(x)-f(x)g'(x)] / [g(x)^2] TERM 8 Laws of Logarithms Log(bc)= DEFINITION 8 Log(b) + Log(c) TERM 9 Laws of LogarithmsLog(b^c)= DEFINITION 9 c*log(b)taking "b" to power "c" scales "log(b)" by a factor of "c" TERM 10 Laws of Exponents(a^x)(a^y)= DEFINITION 10 a^(x+y)