Problems with begginer level calculus

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In summary, the conversation discusses differentiating a function using the power rule, with a discrepancy in the correct answer provided by the textbook. The student believes it to be a typo and the editor encourages reporting any non-trivial errors. The conversation also praises the book as a good resource for beginners in calculus.
  • #1
rustynail
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Hello people! I have bought ''Calculus Made easy'' by Silvanus P. Thompson, I'm starting to teach myself calculus before actually taking the course. The problem discussed here will be about applying the power rule. Also, I'm not quite familiar with the use of LaTeX, so I'll try to make it as clear as possible without it.

Homework Statement



Differentiate the following : y=³√[x^(-5)]

Homework Equations



Just used the power rule really.

The Attempt at a Solution



y = x^(-5/3)

dy/dx = (-5/3)x^[(-5/3)-1]

dy/dx = (-5/3)x^(-8/3)

and I believe I'm finished here.

But the textbook gives a different answer : dy/dx = (-5/3)x^(-8/5)

And I really don't see how they got (-8/5) as a power of x.

thanks for your time.
 
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  • #2
rustynail said:
Hello people! I have bought ''Calculus Made easy'' by Silvanus P. Thompson, I'm starting to teach myself calculus before actually taking the course. The problem discussed here will be about applying the power rule. Also, I'm not quite familiar with the use of LaTeX, so I'll try to make it as clear as possible without it.

Homework Statement



Differentiate the following : y=³√[x^(-5)]

Homework Equations



Just used the power rule really.

The Attempt at a Solution



y = x^(-5/3)

dy/dx = (-5/3)x^[(-5/3)-1]

dy/dx = (-5/3)x^(-8/3)

and I believe I'm finished here.

But the textbook gives a different answer : dy/dx = (-5/3)x^(-8/5)

And I really don't see how they got (-8/5) as a power of x.

thanks for your time.

It must be a typo in the book. You are right.
 
  • #3
thanks for the quick reply!
 
  • #4
rustynail said:
thanks for the quick reply!

Contrasting with the century it has taken to detect and correct this error - or has a new

one been introduced in a reprint?
 
  • #5
epenguin said:
Contrasting with the century it has taken to detect and correct this error - or has a new

one been introduced in a reprint?

''This is a faithful reproduction of the 1914 edition of Calculus Made Easy.''

The editor also notes that any ''non-trivial'' errors should be reported to them.

Should I consider this error to be trivial or not?
 
  • #6
I would report it.
 
  • #7
QuarkCharmer said:
I would report it.

Yes - that is not Making Calculus Easy and other people will get stuck like you; the book is supposed to be for beginners.
 
  • #8
epenguin said:
Yes - that is not Making Calculus Easy and other people will get stuck like you; the book is supposed to be for beginners.

And it's a very good one at that. I recommend it to anyone with interest in the topic.
 

FAQ: Problems with begginer level calculus

What are the common mistakes made in beginner level calculus?

Some common mistakes in beginner level calculus include not understanding the basic concepts, not practicing enough, and not paying attention to details. These mistakes can lead to incorrect solutions and a lack of understanding of the material.

How can I improve my understanding of beginner level calculus?

The best way to improve your understanding of beginner level calculus is to practice regularly and seek help from a tutor or teacher if you are struggling. Additionally, reviewing and understanding the fundamentals of algebra and trigonometry can also greatly improve your understanding of calculus.

What are some tips for solving beginner level calculus problems?

Some tips for solving beginner level calculus problems include setting up the problem correctly, carefully working through each step, and double-checking your work. It is also important to understand the concepts behind the problem rather than just memorizing formulas.

What are the most important concepts to understand in beginner level calculus?

The most important concepts to understand in beginner level calculus are limits, derivatives, and integrals. These concepts form the foundation for more advanced calculus topics and are essential for solving a wide range of problems.

What resources are available for students struggling with beginner level calculus?

There are many resources available for students struggling with beginner level calculus, including online tutorials, textbooks, and study groups. Your teacher or tutor can also provide additional resources and support to help you improve your understanding of the subject.

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