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

1 Answer
divya g.
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#

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