Determine the derivative of $\frac{1}{x}$.

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Lesson Parent: 
Differentiation IV: Differentiation Formulas Everyone Must Know
Problem: 

Determine the derivative of $\frac{1}{x}$.

Answer: 

$f\,'(x)=-\frac{1}{x^2}$

SAMPLE SOLUTION

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Solution: 

Because we have $x$ in the denominator it is best to use the quotient rule. In other words, let's say that

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where <Sign in to see all the formulas> and <Sign in to see all the formulas>. From the quotient rule we know that

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Now we know that <Sign in to see all the formulas> and <Sign in to see all the formulas>. Therefore, we have

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We could have also followed the prescription here and written $f(x)$ as <Sign in to see all the formulas> and used

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to find that

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Both methods are valid and give the same result so pick the method you prefer and keep it in your head for a test.