Problems with begginer level calculus

[rustynail]

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.

 

[Dick]

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.

 

[rustynail]

thanks for the quick reply!

 

[epenguin]

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?

 

[rustynail]

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?

 

[QuarkCharmer]

I would report it.

 

[epenguin]

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.

 

[rustynail]

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.