How do you differentiate #f(x)= (x+5)/ (2x-7 )# using the quotient rule?
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To differentiate ( f(x) = \frac{x + 5}{2x - 7} ) using the quotient rule:
- Let ( u = x + 5 ) and ( v = 2x - 7 ).
- Find the derivatives: ( u' = 1 ) and ( v' = 2 ).
- Apply the quotient rule:
[ f'(x) = \frac{u'v - uv'}{v^2} ]
- Substitute the values:
[ f'(x) = \frac{(1)(2x - 7) - (x + 5)(2)}{(2x - 7)^2} ]
- Simplify the expression to get the final derivative.
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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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