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

Question

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?

Explanation / Answer

Here this is of the type d(u/v) = v.d(u) - u.d(v)/v^2

Hence now for the above problem we get f(x)=x/(x+3)

u=x and v=x+3. Hence f^'(x) = ((x+3)(1)-(x)(1))/(x+3)^2 clearly given by the above formula

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