Not sure I understand basic calculus...

[FlatAssembler]

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))?

[Abaddon_ire]

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

[GrandizerII]

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

[FlatAssembler]

OK, thank you Grandizer!

[LastPoet]

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.

[BrianSoddingBoru4]

Not sure I understand basic calculus...

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

Boru

[Fireball]

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.

[ignoramus]

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!

(yeah, me too)