Question

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

Answer 1

`g'y=2x^(3/2)+(x^2+6)/(2sqrt(x))`

Explanation:

`g(y)=(x^2+6)sqrt(x)=(x^2+6)(x^(1/2))`

Product rule:

`f'(uv)=vu'+uv'`

`u=x^2+6, v=x^(1/2)`

`u'=2x, v'=1/2x^(-1/2)=1/(2sqrt(x))`

`g'y=2x^(3/2)+(x^2+6)/(2sqrt(x))`