I used this in a recent post and maybe thought it would be beneficial to some people to have it posted as a tutorial...hope it helps!

Basic rules

http://www.mathhelpforum.com/math-he...795eda94-1.gif

http://www.mathhelpforum.com/math-he...6602ed7b-1.gif where c is a constant

http://www.mathhelpforum.com/math-he...0a455cb6-1.gif

http://www.mathhelpforum.com/math-he...85206964-1.gif

http://www.mathhelpforum.com/math-he...af8155eb-1.gif...which implies that if the base is e then the derivative is http://www.mathhelpforum.com/math-he...45c4f9d3-1.gif

now we get to some rules

Product rule

http://www.mathhelpforum.com/math-he...f7fe27a0-1.gif where u and v are functions of x

Quotient rule

http://www.mathhelpforum.com/math-he...f32ea4c3-1.gif

Chain rule

http://www.mathhelpforum.com/math-he...17d589c3-1.gif

Now that I have discussed both I will talk about the fact that sometimes easier than the quotient rule is applying the chain rule to quotients by using the fact taht http://www.mathhelpforum.com/math-he...c8ee178e-1.gif...therefore http://www.mathhelpforum.com/math-he...a0d24040-1.gif by the chain rule

Another very useful technique is logarithmic differentiatiow which takes full advantage of logarithims ability to simplify complex functions...this one comes in two flavors...simplification of large quotients...or differentiating when there is an x in the exponent and in the base

I will give you a general case for the second one http://www.mathhelpforum.com/math-he...b7418c56-1.gif..now applying our logarithims(prefably always ln(x) since it is the nicest to work with) we get http://www.mathhelpforum.com/math-he...187d0ec9-1.gif...now using the amazing simplification techniques of logarithim this turns into http://www.mathhelpforum.com/math-he...6cbf33ff-1.gif...now differentiating we get http://www.mathhelpforum.com/math-he...4f9c6c61-1.gif...the right side was gotten using the fact that http://www.mathhelpforum.com/math-he...f74b12b4-1.gif and the left side was gotten using the product rule...and we multiply both sides by y to get the final answer remember that http://www.mathhelpforum.com/math-he...b7418c56-1.gif

for the first use I willshow you an example http://www.mathhelpforum.com/math-he...93cc0a86-1.gif..now using that tecnhique we have http://www.mathhelpforum.com/math-he...815f67df-1.gif...simplifying we get http://www.mathhelpforum.com/math-he...db98cd1b-1.gif...differentiating we get http://www.mathhelpforum.com/math-he...322f6b9c-1.gif...now just multiply both sides by y(the original function) and you have your answer...I will post some practice questions you can work and we can critique you