# Calculus Examples

Check if Differentiable Over an Interval
,
Step 1
Find the derivative.
Find the first derivative.
Rewrite as .
Differentiate using the Power Rule which states that is where .
Rewrite the expression using the negative exponent rule .
The first derivative of with respect to is .
Step 2
Find if the derivative is continuous on .
To find whether the function is continuous on or not, find the domain of .
Set the denominator in equal to to find where the expression is undefined.
Solve for .
Take the square root of both sides of the equation to eliminate the exponent on the left side.
Simplify .
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Plus or minus is .
The domain is all values of that make the expression defined.
Interval Notation:
Set-Builder Notation:
Interval Notation:
Set-Builder Notation:
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