Reflection #15

Right now in calculus we are going back to chapter 3 but im not quite sure on everything so because exams are coming up ill review two important rules.
Both of these rules include a formula.
here is the formula for the product rule:

(recopy the first equation)(take the derivative of the second equation)+(recopy the second equation)(take the derivative of the first equation)

here is a example where you would have to
apply this rule:

(3x-2x^2)(5+4x)

since these two equations are being
multiplied you have to use the product
rule and plug in the formula

After doing so this is what you end up with

(3x-2x^2)(4)+(5+4x)(3-4x)

then you simplify as much as
you can

12x-8x^2+15-20x+12x-16x^2

=-32x^2+4x+15


next is the quotient rule
here is the formula:

(bottom)(derivative of top)-[(top)(derivative of bottom)]/ (bottom)^2

the only way that this rule would not apply is if
you have a number instead of an equation
at the bottom of the fraction.

anyway here is an example using
the quotient rule:

5x^2-2/x^2+1

(x^2+1)(5)-[(5x-2)(2x)/(x^2+1)^2

from here, once again, you just
simplify as much as possible

5x^2+5-[10x^2-4x]/(x^2+1)^2

always keep the bottom of the problem
as is.

5x^2+5-10x^2+4/(x^2+1)^2

=-5x^2+4x+5/(x^2+1)

so it is not too bad as long as you
memorize the formula!