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Not sure I understand basic calculus...
#1
Not sure I understand basic calculus...
I've began to study calculus on the university. I thought I understood it back in high school, but, once I got slightly deeper into it, it turned out I don't.

Here is my question, if the derivative of the inverse function is the reciprocal of the derivative of the function, and the derivative of the arctan function is 1/(1+x*x), how come the derivative of the tangent isn't 1+x*x but is instead 1/(cos(x)*cos(x))?
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#2
RE: Not sure I understand basic calculus...
(February 15, 2019 at 12:00 pm)FlatAssembler Wrote: I've began to study calculus on the university. I thought I understood it back in high school, but, once I got slightly deeper into it, it turned out I don't.

Here is my question, if the derivative of the inverse function is the reciprocal of the derivative of the function, and the derivative of the arctan function is 1/(1+x*x), how come the derivative of the tangent isn't 1+x*x but is instead 1/(cos(x)*cos(x))?

Because the highlighted bit is false.

Consider f(x)=x*x. It's derivative is 2x.

The inverse function is f(x)=sqrt(x). Its derivative is 1/(2*sqrt(x))

2x is not the reciprocal of 1/(2*sqrt(x)) now is it?

ETA: You swapped terms. That's the problem. It's the inverse of the derivative, not the derivative of the inverse you were after. Language matters even in math.

To rework the above example,

Nope, I can't get the plaintext to work for me after several attempts. I give up. You get the point. Its late. I am not about to try to bend ASCII to my will.

Operator precedence matters too
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#3
RE: Not sure I understand basic calculus...
The derivative of the inverse function is the reciprocal of the derivative of the function of the inverse function with respect to the inverse function.

Give me some time, and I'll work it out for you (if no one else does it before me, that is).

EDIT: Here you go:

https://i.imgur.com/Hu855AL.png

(secx)^2 = 1/(cosx)^2
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#4
RE: Not sure I understand basic calculus...
OK, thank you Grandizer!
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#5
RE: Not sure I understand basic calculus...
Now send grandizer a lot of hookers and blow for the help he gave you. Or a rep point if he isn't into it.
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#6
RE: Not sure I understand basic calculus...
Quote:Not sure I understand basic calculus...

I don't have that problem.  I am completely sure I don't understand basic calculus.

Boru
‘Let me never fall into the vulgar mistake of dreaming that I am persecuted whenever I am contradicted.’ Ralph Waldo Emerson
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#7
RE: Not sure I understand basic calculus...
Just remember that for every epsilon, there is a delta. Kind of like for every scraggly horse, there is a scraggly bush. It's cleverly disguised math porn.
If you get to thinking you’re a person of some influence, try ordering somebody else’s dog around.
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#8
RE: Not sure I understand basic calculus...
(February 16, 2019 at 8:45 pm)BrianSoddingBoru4 Wrote:
Quote:Not sure I understand basic calculus...

I don't have that problem.  I am completely sure I don't understand basic calculus.

Boru

Give it a go... it's as easy as pi! Big Grin

(yeah, me too)
No God, No fear.
Know God, Know fear.
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