Calculus Examples

Find the Derivative - d/dx (x^2-9)/(x-3)
Step 1
Differentiate using the Quotient Rule which states that is where and .
Step 2
Differentiate.
Tap for more steps...
Step 2.1
By the Sum Rule, the derivative of with respect to is .
Step 2.2
Differentiate using the Power Rule which states that is where .
Step 2.3
Since is constant with respect to , the derivative of with respect to is .
Step 2.4
Simplify the expression.
Tap for more steps...
Step 2.4.1
Add and .
Step 2.4.2
Move to the left of .
Step 2.5
By the Sum Rule, the derivative of with respect to is .
Step 2.6
Differentiate using the Power Rule which states that is where .
Step 2.7
Since is constant with respect to , the derivative of with respect to is .
Step 2.8
Simplify the expression.
Tap for more steps...
Step 2.8.1
Add and .
Step 2.8.2
Multiply by .
Step 3
Simplify.
Tap for more steps...
Step 3.1
Apply the distributive property.
Step 3.2
Apply the distributive property.
Step 3.3
Apply the distributive property.
Step 3.4
Simplify the numerator.
Tap for more steps...
Step 3.4.1
Simplify each term.
Tap for more steps...
Step 3.4.1.1
Multiply by by adding the exponents.
Tap for more steps...
Step 3.4.1.1.1
Move .
Step 3.4.1.1.2
Multiply by .
Step 3.4.1.2
Multiply by .
Step 3.4.1.3
Multiply by .
Step 3.4.2
Subtract from .
Step 3.5
Factor using the perfect square rule.
Tap for more steps...
Step 3.5.1
Rewrite as .
Step 3.5.2
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
Step 3.5.3
Rewrite the polynomial.
Step 3.5.4
Factor using the perfect square trinomial rule , where and .
Step 3.6
Cancel the common factor of .
Tap for more steps...
Step 3.6.1
Cancel the common factor.
Step 3.6.2
Rewrite the expression.