Differentiate the function. y = (2x^2 + 8x + 6)/√x

Answer 1

Hi Emanuel,

We have by the quotient rule y' = (f'g-g'f)/g², where y=f/g, provided g≠0. Now let f(x)= 2x²+8x+6 and g(x)=√x. So then

y' = (f'g-g'f)/g² (sorry for the formatting)

= ((2x²+8x+6)'(√x)-(√x)'(2x²+8x+6))/(√x)²

=((4x+8)(√x)-(1/2√x)(2x²+8x+6))/x

=(4x^3/2+8x^1/2-x^3/2-4x^1/2-3x^-1/2)/x

=4x^1/2+8x^-1/2-x^1/2-4x^-1/2-3x^-3/2

=3x^1/2+4x^-1/2-3x^-3/2.

Hope that helped.