# Calculus Examples

Find the Derivative Using Quotient Rule - d/dx
Step 1
Differentiate using the Quotient Rule which states that is where and .
Step 2
Differentiate.
By the Sum Rule, the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Since is constant with respect to , the derivative of with respect to is .
By the Sum Rule, the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Since is constant with respect to , the derivative of with respect to is .
Step 3
Simplify.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify the numerator.
Simplify each term.
Multiply by .
Multiply by .
Rewrite using the commutative property of multiplication.
Multiply by by adding the exponents.
Move .
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Subtract from .
Reorder terms.
Simplify the denominator.
Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Apply the product rule to .
Factor out of .
Factor out of .
Factor out of .
Rewrite as .
Factor out of .
Rewrite as .
Move the negative in front of the fraction.