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Derivatives of Rational Function


If f(x)=1x,\displaystyle f(x)=\frac{1}{x}, what is f(x)f'(x)?

If f(x)=1x3,\displaystyle f(x)=\frac{1}{x^3}, what is f(x)f'(x)?

If f(x)=7xx2+7,\displaystyle f(x)=\frac{-7x}{x^2+7}, what is the value of f(3)? f'(3)?

If f(x)=x22x2+1,\displaystyle f(x)=\frac{x-22}{x^2+1}, what is the value of f(1)?f'(-1)?

If f(x)=4x2,\displaystyle f(x)=\frac{4}{x^2}, what is f(x)f'(x)?


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