, Welcome back to Calculus One. And welcome to week six of our time together.
Can you believe that we've been at the Calculus game for more than a month
already? And we've done a ton of stuff so far. Way back at the beginning of the
course, we first met limits. We explored what it meant to evaluate a function near,
but not at, a particular import point. And once we have limits, we were able to
define the derivative. We explore how wiggling the input to a function would
effect the function in some way. That ratio given by the derivative. Then, we
spent a lot of time focusing on how to actually compute the derivative. Alright?
We learned all these derivatives rules of the product rule, and quotient rule last
with the chain rule for actually computing derivative of functions. And this week is
no exception. We continue that proud tradition of actually differentiating. But
in week six, we focus in on the transcendental functions. What are
transcendental functions? Now, most of the functions that we've been looking at thus
far are really algebraic functions. They're, say, polynomials or rational
functions, roots. Transcendental functions are functions that transcend algebra, like
e to the x, or log. Functions that we couldn't have gotten to if all we had at
our disposal was algebra. Another great example of transcendental functions are
sine, cosine, and tangent, the trigonometric functions. And if your not
feeling super comfortable with trig functions, no worries. We're going to
review trig functions this week, as well. But by the end of this week, we're going
to know how to differentiate those trick functions, and that sets us up for week
seven. And what happens in week seven? Applications of the derivative. We're
spending a ton of time focusing on techniques of differentiation, and next
week we'll see some applications. The pay off is going to be huge. Just one more
week of calculations to get through, and then we can see what all of this is used
for. Good luck.