Week 8

This week we learned about the chain rule, u substitution, implicit differentiation and higher order implicit differentiation. The chain says that when you take the derivative of a composite you first take the derivative of the outside and then multiply that by the derivative of the inside. Mathematically that is (fog)'(x)=f'(g(x))•g'(x). It looks more complicated than it really is. U substitution is for finding antiderivatives of composites. Basically you plug in u for whatever is in the parenthesis then find the derivative and find the derivative of u. I understand how it works it's just hard to explain in words. Once I got the hang of these u substitution problems they were kind of fun to do in the homework. Implicit differentiation is when you have y in the problem such as x+2y=5x-y. For this there is like four steps you have to do. First you have to take the derivative of both sides while treating y as a function. Then collect all the terms with y', which is equal to dy/dx, onto one side of the function. After that you have to factor out the y' and then do the algebra so the function is set equal to y'. For the higher order implicit differentiation problems all you have to do is do implicit differentiation as many times as it asks you to. These concepts didn't seem very hard to me but if you miss one step or make one little mistake then it screws up the entire problem. The quiz was somewhat challenging. Number nine was really a struggle. Overall I think I have a pretty good understanding of the concepts though. Hopefully the test won't be too challenging. There was a problem on the quiz with a circle that was kind of confusing but when the equation was written on the board it made it a lot easier to solve.