How do you find the derivative of # f(x)=((18x)/(4+(x^2)))#?
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To find the derivative of ( f(x) = \frac{18x}{4 + x^2} ), you can use the quotient rule, which states that if ( f(x) = \frac{u(x)}{v(x)} ), then ( f'(x) = \frac{u'(x)v(x) - u(x)v'(x)}{(v(x))^2} ). Let ( u(x) = 18x ) and ( v(x) = 4 + x^2 ). Now, find ( u'(x) ) and ( v'(x) ):
( u'(x) = 18 ) ( v'(x) = 2x )
Now, apply the quotient rule:
( f'(x) = \frac{(18)(4 + x^2) - (18x)(2x)}{(4 + x^2)^2} ) ( f'(x) = \frac{72 + 18x^2 - 36x^2}{(4 + x^2)^2} ) ( f'(x) = \frac{72 - 18x^2}{(4 + x^2)^2} )
So, the derivative of ( f(x) ) is ( f'(x) = \frac{72 - 18x^2}{(4 + x^2)^2} ).
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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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