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 .
- 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 and power functions are of the form , where is a positive real number and 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 .
- The formula for differentiating a logarithmic function is .
- The following formulas express the derivatives of sine and cosine