# Calculus Examples

Check if Differentiable Over an Interval
,
Step 1
Find the derivative.
Step 1.1
Find the first derivative.
Step 1.1.1
By the Sum Rule, the derivative of with respect to is .
Step 1.1.2
Evaluate .
Step 1.1.2.1
Since is constant with respect to , the derivative of with respect to is .
Step 1.1.2.2
Differentiate using the Power Rule which states that is where .
Step 1.1.2.3
Multiply by .
Step 1.1.3
Differentiate.
Step 1.1.3.1
Differentiate using the Power Rule which states that is where .
Step 1.1.3.2
Since is constant with respect to , the derivative of with respect to is .
Step 1.1.3.3
Step 1.2
The first derivative of with respect to is .
Step 2
Find if the derivative is continuous on .
Step 2.1
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
Set-Builder Notation:
Step 2.2
is continuous on .
The function is continuous.
The function is continuous.
Step 3
The function is differentiable on because the derivative is continuous on .
The function is differentiable.
Step 4