How do you differentiate #f(x)= (3x^2 + 5x 8 )/ (2x 1 )# using the quotient rule?
Here u go
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To differentiate ( f(x) = \frac{{3x^2 + 5x  8}}{{2x  1}} ) using the quotient rule, follow these steps:

Identify ( u ) and ( v ): ( u = 3x^2 + 5x  8 ) ( v = 2x  1 )

Compute ( u' ) and ( v' ): ( u' = 6x + 5 ) ( v' = 2 )

Apply the quotient rule: ( f'(x) = \frac{{u'v  uv'}}{{v^2}} )

Substitute into the formula: ( f'(x) = \frac{{(6x + 5)(2x  1)  (3x^2 + 5x  8)(2)}}{{(2x  1)^2}} )

Expand and simplify: ( f'(x) = \frac{{12x^2 + 10x  6x  5  6x^2  10x + 16}}{{(2x  1)^2}} )

Combine like terms: ( f'(x) = \frac{{6x^2  5}}{{(2x  1)^2}} )
Therefore, the derivative of ( f(x) ) with respect to ( x ) is ( f'(x) = \frac{{6x^2  5}}{{(2x  1)^2}} ).
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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