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How do you differentiate #g(x) =(x^2 + 6) (x^2 + 1)^5 # using the product rule?

1 Answer

Shwetank Mauria

May 11, 2016

#d/dxg(x)=2x(x^2+1)^4(6x^2+31)#

Explanation:

#d/dx(p(x)*q(x))=(dp)/dx*q(x)+(dq)/dx*p(x)#

Hence #d/dxg(x)=(2x)*(x^2+1)^5+(x^2+6)*5(x^2+1)^4*2x#

= #2x(x^2+1)^5+10x(x^2+6)(x^2+1)^4#

= #2x(x^2+1)^4{(x^2+1)+5(x^2+6)}#

= #2x(x^2+1)^4(6x^2+31)#

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