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))?
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))?
