# Calculus Examples

,

Step 1

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

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