Post #27

I CAN'T BELIEVE WE HAVE SCHOOL TOMORROW!...HOPE EVERYONE HAD A GREAT HOLIDAY!


TO TAKE A DERIVATIVE take the exponent and multiply it by the coeffient to make a new coeffient, then subtract one from the exponent for the new exponent and that's your derivative!


TO TAKE AN INTEGRAL take the exponent and add one, then take it's reciprical and multiply it by the coeffient to make the new coeffient. that's the integral!


LIMITS:
~If the degree on top is the same as the degree on the bottom, you divide the coefficients to get the limit.
~If the degree on top is bigger than the degree on the bottom, then the limit is infinity.~If the degree on top is smaller than the degree on the botton, then the limit is zero.


PRODUCT RULE:
the product rule is used when two things are being multiplied together.
copy the first times the derivative of the second PLUS copy the second times the derivative of the first
for example:
Find the derivative of (2x)sin(x)
2(cos(x)) + sin(x)(2) =
4cos(x)+sin(x)


QUOTIENT RULE:
the quotient rule is used when there's something being divided by something and you need to take a derivative you copy the bottom times the derivative of the top MINUS the top times the derivative of the bottom all over the bottom squared
for example:
Find the derivative of (2x^2) over (x)
(x)(4x)-(2x^2)(1) all over (x^2)
(4x^2)-(2x^2) all over (x^2)
therefore: (2x^2) over (x^2) givis you 2 for the derivative


CHAIN RULE:
the chain rule is used when you are finding the derivative with exponents.
*work from the outside in.
Example: sin^2 (x^2)
2(sin (x^2))(cos (x^2)(2x)
4x sin(x^2)cos(x^2)

~ElliE~