Calculus Examples

Find the Derivative - d/dx x(6-2x)^2
Step 1
Rewrite as .
Step 2
Expand using the FOIL Method.
Tap for more steps...
Step 2.1
Apply the distributive property.
Step 2.2
Apply the distributive property.
Step 2.3
Apply the distributive property.
Step 3
Simplify and combine like terms.
Tap for more steps...
Step 3.1
Simplify each term.
Tap for more steps...
Step 3.1.1
Multiply by .
Step 3.1.2
Multiply by .
Step 3.1.3
Multiply by .
Step 3.1.4
Rewrite using the commutative property of multiplication.
Step 3.1.5
Multiply by by adding the exponents.
Tap for more steps...
Step 3.1.5.1
Move .
Step 3.1.5.2
Multiply by .
Step 3.1.6
Multiply by .
Step 3.2
Subtract from .
Step 4
Differentiate using the Product Rule which states that is where and .
Step 5
Differentiate.
Tap for more steps...
Step 5.1
By the Sum Rule, the derivative of with respect to is .
Step 5.2
Since is constant with respect to , the derivative of with respect to is .
Step 5.3
Add and .
Step 5.4
Since is constant with respect to , the derivative of with respect to is .
Step 5.5
Differentiate using the Power Rule which states that is where .
Step 5.6
Multiply by .
Step 5.7
Since is constant with respect to , the derivative of with respect to is .
Step 5.8
Differentiate using the Power Rule which states that is where .
Step 5.9
Multiply by .
Step 5.10
Differentiate using the Power Rule which states that is where .
Step 5.11
Multiply by .
Step 6
Simplify.
Tap for more steps...
Step 6.1
Apply the distributive property.
Step 6.2
Combine terms.
Tap for more steps...
Step 6.2.1
Move to the left of .
Step 6.2.2
Raise to the power of .
Step 6.2.3
Raise to the power of .
Step 6.2.4
Use the power rule to combine exponents.
Step 6.2.5
Add and .
Step 6.2.6
Subtract from .
Step 6.2.7
Add and .
Step 6.3
Reorder terms.