How do you differentiate #f(x)= (1-3x^2)^4* (1-x+7x^2)^4 # using the product rule?

1 Answer
May 27, 2017

Answer:

#f'(x)=4(1-x+7x^2)^3(1-3x^2)^3(-84x^3+9x^2+8x-1)#

Explanation:

#f(x)=(1-3x^2)^4*(1-x+7x^2)^4#
Using product rule,
#f'(x)=(1-3x^2)^4*d/dx(1-x+7x^2)^4+(1-x+7x^2)^4*d/dx(1-3x^2)^4#
Now,
#d/dx(1-x+7x^2)^4=4(1-x+7x^2)^3*d/dx(1-x+7x^2)=4(1-x+7x^2)^3(14x-1)#
and,
#d/dx(1-3x^2)^4=4(1-3x^2)^3*d/dx(1-3x^2)=4(1-3x^2)^3(-6x)#
Put these two values in the expression for f'(x) and extract the common terms to get,
#f'(x)=4(1-x+7x^2)^3(1-3x^2)^3[(1-3x^2)(14x-1)-6x(1-x+7x^2)]#
Further solving the equation we get, #f'(x)=4(1-x+7x^2)^3(1-3x^2)^3(-84x^3+9x^2+8x-1)#
which is the final answer