, 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.