Blog 11

Alright, so this week wasn’t too bad, we’ve been able to do a lot of things to get our grade up which is really helpful :). We also started learning chapter five, which is pretty simple but can get hard just like everything else we learn in calculus. It still deals with derivatives but it goes back to simple concepts, like exponents and logs. *So you will have to review all of those rules before trying to work the problems. You want to make them as simple as possible before taking the derivative of a problem.

Section 5.1: d/dx ln u=1/u(du)

Example: d/dx= ln (2x)= 1/2x(2)=1/x
d/dx= ln(x^2+1)=1/x^2+1(2x)=2x/x^2+1
-For these problems you just put the number behind ln in the denominator, and leave it as it is. Then multiply it by the derivative of that number. They also have problems like this that involve chain rule, and product rule.

Here are some examples using log rules:
Expand:
ln xy/z=ln(x)(1)+(y)(1)-ln z
-Using the log rules when something is multiplied it means add, when something is divided it means subtract. This one also uses the product rule.
Condense:
ln(x-2)-ln(x+2)=ln(x-2)/(x+2)

The exponential functions are pretty much the same as the log ones.
d/dx=e^u=e^u(du/dx)
-Recopy the problem, then times it by the derivative of u.

Examples:
E^2x-1=e^2x-1(2)=2e^2x-1
E^-3/x=e^-3/x(3/x^2)=3e^-3/x/x^2
Rules to remember for exponential functions:
ln e^x=4, x=4
e^lnx^2=9, x=+/- 3
e^x=5, x=ln 5

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Something that's still giving me trouble is using more than one rule together in these problems. I get confused when the chain rule and product rule get mixed, then when they throw in trig functions I just get even more confused. I think I just need more practice on this.