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How do you differentiate #f(x)=(3x)/(x-2)-6/(x-2)# using the quotient rule?

Answer 1

Emilia Aguilar

#dy/dx=0#

Given -

#y=(3x)/(x-2)-6/(x-2)#

Since #x-2# is common to both fractions

#y=(3x-6)/(x-2)#

#dy/dx=([(x-2)(3)]-[(3x-6)(1)])/(x-2)^2# #dy/dx=([3x-6]-[3x-6])/(x-2)^2# #dy/dx=(3x-6-3x+6)/(x-2)^2# #dy/dx=0/(x-2)^2=0#

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Answer 2

Ezekiel Alexander

To differentiate the function ( f(x) = \frac{3x}{x-2} - \frac{6}{x-2} ) using the quotient rule:

Identify ( u(x) = 3x ) and ( v(x) = x - 2 ).
Apply the quotient rule: ( \frac{d}{dx} \left( \frac{u(x)}{v(x)} \right) = \frac{v(x) \cdot u'(x) - u(x) \cdot v'(x)}{(v(x))^2} ).
Find ( u'(x) ) and ( v'(x) ) by taking the derivatives of ( u(x) ) and ( v(x) ), respectively.
Substitute the values into the quotient rule formula.
Simplify the expression.

The derivative of ( f(x) ) with respect to ( x ) using the quotient rule will be the simplified result.

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Answer from HIX Tutor

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