# Calculus Examples

Step 1

Set as a function of .

Step 2

Step 2.1

Since is constant with respect to , the derivative of with respect to is .

Step 2.2

Differentiate using the Power Rule which states that is where .

Step 2.3

Multiply by .

Step 3

Step 3.1

Divide each term in by and simplify.

Step 3.1.1

Divide each term in by .

Step 3.1.2

Simplify the left side.

Step 3.1.2.1

Cancel the common factor of .

Step 3.1.2.1.1

Cancel the common factor.

Step 3.1.2.1.2

Divide by .

Step 3.1.3

Simplify the right side.

Step 3.1.3.1

Divide by .

Step 3.2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

Step 3.3

Simplify .

Step 3.3.1

Rewrite as .

Step 3.3.2

Pull terms out from under the radical, assuming positive real numbers.

Step 3.3.3

Plus or minus is .

Step 4

Step 4.1

Replace the variable with in the expression.

Step 4.2

Simplify the result.

Step 4.2.1

Raising to any positive power yields .

Step 4.2.2

Multiply by .

Step 4.2.3

The final answer is .

Step 5

The horizontal tangent line on function is .

Step 6