Differentiate the function = (3 2+2) 2√6+2
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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
=(4x3/2+8x1/2-x3/2-4x1/2-3x-1/2)/x
=4x1/2+8x-1/2-x1/2-4x-1/2-3x-3/2
=3x1/2+4x-1/2-3x-3/2.
Step-by-step explanation:
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