Question

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

Answer 1

`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)`