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

Definitions and rules for various concepts in calculus, including l'hopital's rule, chain rule, product rule, quotient rule, implicit differentiation, laws of logarithms, laws of exponents, and critical points. These concepts are essential for understanding derivatives and their applications.

Typology: Quizzes

2010/2011

Uploaded on 04/20/2011

christopher-gowen
christopher-gowen 🇺🇸

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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 giv en "explicitly" in terms of the
independent variable. y'(x) = dy/dx1.) differentiate both sides
w.r.t. "x", writting "y" as "y(x)" using ch ain rule2.) solve for
"y'(x)"3.) plug in "y" and "x" values
pf3
pf4

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L'Hpital's rule

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

What rule should be used to solve d/dx

f(x)g(x)?

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)

Linear approximation and error

Definition