$\rhd$ Basic derivative rules (Part 1) (2:26) The derivative of a constant function, $f(x) =k$, using the limit definition and a geometric approach.
* Practice: A summary of the differentiation rules – sum, difference, product and quotient. (4 problems)
$\rhd$ Basic derivative rules: table(8:59) A table with the values of $f(x)$ and $f'(x)$ are given for $x=0, 1, 4, 9, 16$. The functions $g$ and $h$ are defined as $g(x) = |x-1|+1$ and $h(x) = 3f(x)+2g(x)$. Find $\dfrac{d}{dx}h(x)$ at $x=9$, or equivalently, $h'(9)$.
$\rhd$ Power rule (3:53) The derivative of $x^n$ when $n\neq 0$. Examples shown: $x^2$, $x^3$, $x^{-100}$, $x^{2.572}$.
$\rhd$ Basic derivative rules (9:52) The derivative of a sum of power functions or power functions multiplied by a constant. Find the derivative of $2x^5$, $x^3+x^{-4}$ and $2x^3-7x^2+3x-100$.
$\rhd$ Product rule (8:03) Find the derivative of $h(x) = (x^2)(x^3+4)$ (first 3:20 minutes) and $y= (\sin x)(\cos x) (x^2+1)$ (can be skipped if you have not seen the derivative of trig functions).
Quotient Rule
$\rhd$ Quotient rule (7:37) Find the derivative of $y=\dfrac{x^2+1}{x^5+x}$ (first 3:34 minues) and $y=\dfrac{\tan x}{x^{3/2}+5x}$ (can be skipped if you have not seen the derivative of trig functions).
