Blog 7

So this week we sorta reviewed chapter 2, derivatives, and tried out related rate problems, which are hard to grasp depending on the structure of the word problems.

Finding a derivative of a function, in my words, is like this: the more that is going on in the problem, the more work needed and more steps taken to find it. Ex: the chain rule

if you're asked to find the slope of a tangent line, dy/dx, f'(x), instantaneous velocity, it simply means take the derivative.

My interpretation on the Rules of derivatives:
1. if there is a constant, the derivative of a constant=0 f(5)=5 f'(5)=0

2. when there is an exponent on a variable, you multiply by the exponent and subtract 1 from the exponent Ex: f'(3x^2)=6x

3.when there is a fraction, bottom(f'(top)-[top(f'bottom)]/bottom^2

4.when there is multiplication involved, 1st(f'2nd)+2nd(f'1st)

5.when there is more than one operation (3x+4)^2, bring exponent to the front, recopy inside, multiply by f'inside
2(3x+4)(3)
6(3x+4)=18x+24

6.when trig is involved, remember those identities to simplify as much as possible (tricky)

7.when there is more than one variable (implicits) you solve for dy/dx using algebra

8.when there is a word probelm, *sigh* related rates can get confusing depending on the setup and the geometry used (like the ones about the pool...yuck), you start by finding the rate, setting up the information, then start using geometry with derivatives and the complex and the formulas and the oh you know what i mean!
well exams are tomorrow so back to studying