How do you use the quotient rule to differentiate #y=(x+3)^2/(x-1)#?

Answer 1

#f= (x+3)^2, g=x-1->f'=2(x+3)*1=2x+6,g'=1 ->y'=((gf'-fg')/g^2) =( (x-1)(2x+6)-(x+3)^2)/(x-1)^2 =(2x^2+4x-6-x^2-6x-9)/(x-1)^2 = (x^2-2x-15)/(x-1)^2 #

Separate f and g and find their derivatives then plug it in to the quotient rule as shown above

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Answer 2

Charles Anctil

To differentiate ( y = \frac{{(x+3)^2}}{{x-1}} ) using the quotient rule, you would apply the formula:

[ \frac{{d}}{{dx}}\left(\frac{{u}}{{v}}\right) = \frac{{v \cdot u' - u \cdot v'}}{{v^2}} ]

where ( u = (x+3)^2 ) and ( v = x-1 ).

Then, calculate ( u' ) and ( v' ) using the power rule and constant rule, respectively:

[ u' = 2(x+3) ] [ v' = 1 ]

Finally, substitute these values into the quotient rule formula to find the derivative of ( y ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.