- Derivative of the function "integer power", using Newton's binomial.
therefore, if ,
- Derivative of the sum, substraction and multiplication times a number: "linearity"... by now we only can do polynomials!!
- What about product of functions? Leibniz Rule,
let's check whether it works with two monomials
- What happens when the power is not an integer? Case of the square root or 1/x... we accept by now the extension of the rule...
- Exponential function, special value of "e"
- And the logarithm? Let's check the inverse function...
- And the compound function? Chain rule,
What does it really mean?
Let's check a simple example:
- Now, with exp and log, let's return to the power of real exponent
OK! It's coherent!!
- Go on with trigonometric functions
starting with when ,
- Summary of rules and applications
New terms: Leibniz rule, Chain rule