Common Calculus Mistakes

mathmistakes.info
Your Resource for Stronger Math Skills

Common Calculus Mistakes
Real Mistakes from Real Student Work

Find the calculus mistakes in these examples and read plain language explanations so you can avoid making these same mistakes yourself!

Limits

Example 1
Example 2 (l'Hôpital's rule)
Example 3 (l'Hôpital's rule)
Example 4 (l'Hôpital's rule)

Limit Definition of the Derivative
(also see the f(a+h) and f(x+h)
Examples in the "Function
Notation" section of Common Algebra Mistakes)

Example 1

Power Rule

Example 1
Example 2
Example 3 (with parameters)

Derivatives of:

Exponential Functions

Trigonometric Functions

Example 1 (Secant)

Inverse Trigonometric Functions

Example 1 (Inverse sine)
Example 2 (Inverse tangent)

Hyperbolic Functions

Example 1 (Hyperbolic cosine)
Example 2 (Hyperbolic sine)

Derivative Rules:

Sum Rule

Example 1 (Constants)

Product Rule

Example 1 (Constant Multiple)
Example 2 (Constants)
Example 3 (Constants)

Quotient Rule

Chain Rule

Example 1 (Power Rule)
Example 2 (Power Rule)
Example 3 (Power Rule)
Example 4 (Power Rule)
Example 5 (Cosine)
Example 6 (Inverse sine)
Example 7 (Inverse sine)
Example 8 (Inverse tangent)
Example 9 (Exponential)
Example 10 (Exponential)
Example 11 (Natural Logarithm)
Example 12 (Natural Logarithm)
Example 13 (Compound Chain Rule)
Example 14 (Compound Chain Rule)

Tangent Lines

Example 1

Implicit Differentiation

Indefinite Integrals (Antiderivatives)

Example 1 (Exponential)
Example 2 (Sine)
Example 3 (Cosine)

Definite Integrals

Example 1

Area Under a Curve or Between Curves

Example 1

Derivative of an Integral

Example 1

Multivariable Calculus

Partial Derivatives

Example 1 (Quotient Rule)
Example 2 (Tangent)

Don't forget to also visit Common Algebra Mistakes and Common Trigonometry Mistakes (many of those mistakes were made by calculus students).

More examples will be added, so be sure to come back and visit again soon.

Also visit Calculus Facts Flashcards and other resources

Now available: common calculus mistakes t-shirt displays mistakes from this list. It's a great gift for students and teachers.

MultimediaComing Soon!	BlogThe webmaster's blog discusses mathmistakes.info content as well as issues in mathematics education and other mathematics topics	DiscussionComing Soon	NewslettersComing Soon	About this SiteDescription of the content and goals of the calculus mistakes section of mathmistakes.info	LinksLinks to other calculus help web sites
ProductsSite-related merchandise. Find a unique gift for a teacher, student, friend or yourself	BrowsersBrowser recommendations and known browser compatibility issues	Terms of UseTerms of Use of the mathmistakes.info web site	Privacy PolicyThe privacy policy of mathmistakes.info	Help this SiteHow you can help mathmistakes.info	Special OffersA collection of sponsored links all on one page

Home Page |

If you like mathmistakes.info and/or find it useful, please consider making a secure donation by clicking on the button at right (Paypal account not required). Your donation will help keep mathmistakes.info online. Click here for other ways to help mathmistakes.info.

Save This Page