How do you differentiate #y=(x+3)^2/(x-1)#?

Answer 1

#dy/dx = ((x-5)(x+3))/(x-1)^2#

#y = (x+3)^2/(x-1)#
The quotient rule states that if #y = f(x)/g(x)#
Then #dy/dx = (g(x)*f'(x) - f(x)*g'(x))/(g(x))^2#
Using the quotient rule in this example: #dy/dx#= #((x-1)*2(x+3)*1 - (x+3)^2*1) / (x-1)^2#
#dy/dx = (2(x^2+2x-3) - (x^2+6x+9)) / (x-1)^2#
#dy/dx= (x^2-2x-15)/(x-1)^2#
#dy/dx= ((x-5)(x+3))/ (x-1)^2#
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Answer 2

To differentiate ( y = \frac{{(x+3)^2}}{{x-1}} ), you can use the quotient rule, which states that if ( y = \frac{{f(x)}}{{g(x)}} ), then ( y' = \frac{{f'(x)g(x) - f(x)g'(x)}}{{[g(x)]^2}} ). Apply this rule to find the derivative of the given function.

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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.

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.

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.

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.

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