# Calculus Examples

Check if Differentiable Over an Interval
,
Step 1
Find the derivative.
Step 1.1
Find the first derivative.
Step 1.1.1
Rewrite as .
Step 1.1.2
Differentiate using the Power Rule which states that is where .
Step 1.1.3
Rewrite the expression using the negative exponent rule .
Step 1.2
The first derivative of with respect to is .
Step 2
Find if the derivative is continuous on .
Step 2.1
To find whether the function is continuous on or not, find the domain of .
Step 2.1.1
Set the denominator in equal to to find where the expression is undefined.
Step 2.1.2
Solve for .
Step 2.1.2.1
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 2.1.2.2
Simplify .
Step 2.1.2.2.1
Rewrite as .
Step 2.1.2.2.2
Pull terms out from under the radical, assuming positive real numbers.
Step 2.1.2.2.3
Plus or minus is .
Step 2.1.3
The domain is all values of that make the expression defined.
Interval Notation:
Set-Builder Notation:
Interval Notation:
Set-Builder Notation:
Step 2.2
is not continuous on because is not in the domain of .
The function is not continuous.
The function is not continuous.
Step 3
The function is not differentiable on because the derivative is not continuous on .
The function is not differentiable.
Step 4