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FunctionProvide an example on how to differentiate a fraction, if the maxim power of...
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example function : f(x)=(3x+14)/(3x^2+7x)
Since the given function is a quotient, we'll apply the quotient rule to find it's first derivative:
(u/v)' = (u'*v - u*v')/v^2 (*)
We'll put u = 3x+14 => u' = 3
We'll put v = 3x^2 + 7x => v' = 6x + 7
We'll substitute u,v,u',v' in the formula (*):
f'(x) = [3(3x^2 + 7x) - (3x+14)(6x + 7)]/(3x^2+7x)^2
We'll remove the brackets:
f'(x) = (9x^2 + 21x - 18x^2 - 21x - 84x - 98)/(3x^2+7x)^2
We'll combine and eliminate like terms:
f'(x) = -(9x^2 + 84x + 98)/(3x^2+7x)^2
Posted by giorgiana1976 on April 14, 2011 at 7:14 AM (Answer #2)
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