RE: Not sure I understand basic calculus...
February 15, 2019 at 6:22 pm
(This post was last modified: February 15, 2019 at 7:26 pm by Abaddon_ire.)
(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
