blog 4

This week we learned about the product rule and the quotient rule of derivatives
For each of these things you need to use the exact formula needed for the equation. If you do the equation wrong then your answer will be wayyyyy off.
The product rule:
The product rule is recognized as F(x)G(x)
The formula for solving with the product rule is
D/Dx [F(x)G(x)] = F(x) Gprime(x) + G(x) Fprime(x)
First I take the derivative e of each so that when I plug in I already know what the derivatives are to be plugged in
The quotient rule looks like F(x)/G(x)

There might be several types of equations in each problem
The formula for solving with the quotient rule is

D/Dx [F(x)/G(x)] = G(x) Fprime(x)- F(x) Gprime(x)/ [G(x)]^2
When you are solving with the quotient rule the negative must be distributed to the entire product of f(x)G prime(X)

D/Dx [3x-2x^2]= 3-4x
Therefore F prime= 3-4x
D/Dx [5+4x]= 4
Therefore G prime= 4
Now you plug into the formula
3x-2x^2(4)+ 5+4x (3-4x)
12x^2x-8x^2+15-20x+12x-16
-24x^2 + 4x +15
and your answer is
Dx= -24x^2+4x+15

Example: 5x-2/x^2-1
First I take the derivative of each so that when I plug in I already know what the derivatives are to be plugged in
D/dx [ 5x-2] = 5
Therefore F prime= 5
D/dx [x^2 – 1] = 2x
Therefore G prime = 2x
Now you plug into the formula
(x^2+1)(5)-[(5x-2)(2x)]/(x^2+1)^2
5x^2+5-[10x^2-4x]/(x^2+1)^2
5x^2+5-10x^2+4x/(x^2+1)^2
-5x^2 + 4x+5/ (x^2+1)^2
So now your final answer is.
DX= -5x^2 + 4x+5/ (x^2+1)^2