Derivative Rules
Here is the list of different rules for converting a function into a derivative. Use these for conversions of the first, second, third derivative and so on.
The Power Rule
x^n = n•x^(n-1) Example: d/dx x^2 = 2x
The "e" Rule
e^x = e^x Example: 2e^x = 2e^x
The Exponential Rule
n^x = ln(x) • n^x Example: 5^x = (ln 5) • 5^x
The Natural Log Rule
ln(x) = 1/x
The Logarithmic Rule
log a (x) = 1/[x•ln(a)]
Trig Derivative Rules
Chain, Product, & Quotient Rule
These are the problems dealing with a function within a function, a function divided by a function, or a function times another function. Check them out below.
Sample Problem
Here is an example of the rules being used to find the derivatives. This problem encompasses all the derivative rules.
If you go through the list of rules you will find that this covers al the basic derivative rules.
The answer is:
The answer is:
If you can't figure out how this was done, look at the conversion systems.
Cool Looking Links For Further Analysis
http://tutorial.math.lamar.edu/pdf/Calculus_Cheat_Sheet_Derivatives_Reduced.pdf