Determine the derivative of $f(x)=\sqrt{x}$.

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Lesson Parent: 
Differentiation II: The Gory Details of Calculating Derivatives
Problem: 

Determine the derivative of $f(x)=\sqrt{x}$.

Answer: 

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

SAMPLE SOLUTION

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Solution: 

Recall that the derivative is defined as

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For the function <Sign in to see all the formulas> we have

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Let's multiply the numerator and denominator by <Sign in to see all the formulas>:

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Note that we have proven the last equality here.

Therefore,

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