This week in Calculas AB we learned the difference between average velocity, velocity and instantaneous velocity. Average velocity implies finding the slope; instantaneous velocity means to take the derivative. Also, we learned product and quotient rules:
Product Rule:
[f(x)g(x)]=f(x)g1(x)+g(x)f1(x)
Quotient Rule:
[f(x)/g(x)]= g(x)f1(x)-[f(x)g1(x)]/g(x)2
The product and quotient rules are pretty simple. All you do is plug into them.
Ex 1. [(x2+4)(x-2)]
=(x2+4)(1)+(x-2)(2x)
=(x2+4)+(2x2-4x)
=3x2-4x+4
Ex 2. [(x2+4)/(x-2)]
=(x-2)(2x)-[(x2+4)(1)]/(x-2)2
=2x2-4x-x2-4/(x-2)2
=x2-4x-4/(x-2)2
=(x-4)(x+1)/(x-2)2
The last thing we went over was taking the 2nd and 3rd derivative; all you do is take a derivative two or three times. Second and third derivative are represented like say g-prime or g1, but instead of 1, it is 11 or 111-> g11 or g111.
Ex 1. y11[x2]
y1=2x
y11=2
Ex 2. y111[x2]
y1=2x
y11=2
y111=0
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