Differentiate.. A Problem Solving/Inquiry Question

[mathitup]

this example incorporates all of the different differentiation techinques, but I am confused as of where to start....

The question is as follows:

y = x^2(1-x)^3 / (1+x)^3

I am not sure whether to use the prduct rule first or the quotient rule..

 

[tkhunny]

It makes no difference. Unique answer don't care how you find them.

y = x^2(1-x)^3 / (1+x)^3

It can be helpful to rewrite it a little.

f(x) = x^2(1-x)^3
g(x) = (1+x)^3

Then

y = f(x)/g(x)

Can you write the general formula for the quotient rule and then find all the parts and plug them in?

 

[soroban]

Hello, mathitup!

. . . . .x²(1 - x)³
y .= .-------------
. . . . . (1 + x)³

I am not sure whether to use the product rule first or the quotient rule.

Well, you have a <u>quotient</u>.
The product comes up while you're using the Quotient Rule.

If you use the Product Rule first, how would you work in the denominator?