1.8, The IRC of Transcendental Functions

In this lecture (of Friday, Feb 3), we develop the IRC (or derivative) of three fundamental transcendental functions.

In order to do this, we need the limits of

(sin h)/h, 

(1 - cos h)/h,

and

(e^h-1)/h 

as h goes to zero.

We use these limits to then show that the IRC of

f(x) = sin x

at a point x=x0 is

f '(x0) = cos x0;

the IRC of

f(x) = cos x

at a point x=x0 is

f '(x0) = –sin x0 

and the IRC of

f(x) = e^x

at x=x0 is

f'(x0) =  e^x0.

We will use these results throughout the course.  This lecture demonstrates how we found these answers using the definition of the derivative.