How do you Differentiate y = x^2(1-x^3)/(1+x)^3 ?

1 Answer
Mar 2, 2018

Basically, you go ahead using the quotient rule and product rule of differentiation for this answer, step by step
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Explanation:

from the above, consider the following analogies in our example:
f(x)= x^2 , g(x)=(1-x^3), j(x)= x^2(1-x^3) and h(x)=(1+x)^3

Let p(x)= [x^2(1-x^3)]/(1+x)^3
Applying product rule to f(x) & g(x) in numerator, and apply quotient rule on j(x) & h(x)

Then p'(x) = {[2x(1-x^3) -3x^4](1+x^3) - 3(1+x)^2x^2(1-x^3)}/(1+x)^6

Simplifying by taking (1+x)^2 common in the numerator, we get:

{[2x(1-x^3)-3x^4](1+x)-3x^2(1-x^3)}/(1+x)^4
Open and solve the brackets in the numerator, solve terms with like degrees of x, and get:
[-2x^5 -x^22 -5x^4 +2x]/(1+x)^4