Category 2: Product Rule Q: f(x)=(x+3)(2x-5) A: f^\' (x)=1(2x-5)+2(x+3)=2x-5+2x+

Question

Category 2: Product Rule

Q: f(x)=(x+3)(2x-5)
A: f^' (x)=1(2x-5)+2(x+3)=2x-5+2x+6=4x+1
RULE SIMPLIFY ANSWER


Q: f(x)=(x^2+4x-2)(5x-7)
A: f^' (x)=5(x^2+4x-2)+(2x+4)(5x-7)=5x^2+20x-10+10x^2-14x+20x-28=15x^2+26x-38


Q: f(x)=2x?x
A: f^' (x)=1/(2?x) (2x)+2(?x)=x/?x+2?x=?x+2?x=3?x
RULE SIMPLIFYING ANSWER

What Rule or Process can you develop that can be used to solve any category two problem?













Category 3: Quotient Rule

Q: f(x)=x/(x+3) 3) Q: f(x)=x^2/(x^2-5)
A: f^' (x)=((x+3)(1)-(x)(1))/(x+3)^2 =3/(x+3)^2 A: f^' (x)=((x^2-5)(2x)-(x^2 )(2x))/(x^2-5)^2 =(-10x)/(x^2-5)^2
RULE Answer RULE ANSWER




Q: f(x)=(x^3+4)/(x^2+5)
A: f^' (x)=((x^2+5)(3x^2 )-(x^3+4)(2x))/(x^2+5)^2 =(x^4+15x^2-8x)/(x^2+5)^2
RULE ANSWER



What Rule or Process can you develop that can be used to solve any category two problem?










Category 4: Chain Rule

Q: f(x)=(2x+1)^3
A: f^' (x)=(2)(3) (2x+1)^2=6(2x+1)^2
Rule Answer


Q: f(x)=?(3x-1)
A: f^' (x)=(3)(1/2) (3x-1)^(-1/2)=3/(2(3x-1)^(1/2) )=3/(2?(3x-1))
Rule Answer


Q: f(x)=(3x^2+2x)^5
A: f^' (x)=(6x+2)(5) (3x^2+2x)^4=(30x+10?)(3x^2+2x)?^4
Rule Answer


Q: f(x)=7/(x^2-4)^6
A: f^' (x)=7(2x)(-6) (x^2-4)^(-7)=-84x/(x^2-4)^7
Rule Answer


What rule or process can you develop to solve any problem like those above? How is the power rule used in this process?

Explanation / Answer

This link contain all the information regarding derivatives and power rules. such as quotient rule, product rule etc.

http://www.columbia.edu/itc/sipa/math/calc_rules_func_var.html

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