Determine the derivative of f(x)=√x.

Primary tabs

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

Determine the derivative of f(x)=√x.

Answer: 

f′(x)=12√x

SAMPLE SOLUTION

All of our problems have fully worked out, logical solutions. We connect every solution to its underlying lesson so you can understand the concepts needed to solve any problem and reinforce your learning by practicing with similar problems. All of the formulas are available to our subscribers, but here is a sample of the problem solution you will see when you log in:



Solution: 

Recall that the derivative is defined as

<Sign in to see all the formulas>


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

<Sign in to see all the formulas>

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

<Sign in to see all the formulas>


Note that we have proven the last equality here.

Therefore,

<Sign in to see all the formulas>