Here are the main points that are addressed in the video. Please read these and think about them as you watch.

• The derivative of a constant function is zero because constant functions have a rate of change of zero at all input values in their domain.
• The power rule is used when you want to compute the derivative of a monomial function (i.e., power function) or a polynomial function. The output of a monomial function consists of a coefficient and an input variable to some integer power. A polynomial function is a sum of monomial functions.
• The power rule says $\dfrac {d}{dx}(x^n) = nx^{n-1}$.
• The derivative of a polynomial function is the derivative of each monomial in the sum. In other words, a derivative of a sum of monomials is the sum of the derivatives.
• Exponential functions are of the form $f(x) = a^x$ and power functions are of the form $f(x) = x^n$, where $a$ is a positive real number and $n$ is an integer. The power rule only applies to differentiating a power function. There is a different formula for computing the derivative of an exponential function.
• The formula for differentiating an exponential function is $\dfrac {d}{dx}(a^x) = a^x \ln (a)$.
• The formula for differentiating a logarithmic function is $\dfrac {d}{dx}(\log _a(x)) = \dfrac {1}{x \ln (a)}$.
• The following formulas express the derivatives of sine and cosine respectively:

  $\dfrac {d}{dx} \sin (x) = \cos (x)$

  $\dfrac {d}{dx} \cos (x) = - \sin (x)$