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Calculus Examples
Step 1
Differentiate using the Product Rule which states that is where and .
Step 2
The derivative of with respect to is .
Step 3
Step 3.1
By the Sum Rule, the derivative of with respect to is .
Step 3.2
Since is constant with respect to , the derivative of with respect to is .
Step 3.3
Differentiate using the Power Rule which states that is where .
Step 3.4
Multiply by .
Step 3.5
Since is constant with respect to , the derivative of with respect to is .
Step 3.6
Differentiate using the Power Rule which states that is where .
Step 3.7
Multiply by .
Step 3.8
Since is constant with respect to , the derivative of with respect to is .
Step 3.9
Differentiate using the Power Rule which states that is where .
Step 3.10
Multiply by .
Step 4
Step 4.1
Apply the distributive property.
Step 4.2
Apply the distributive property.
Step 4.3
Combine terms.
Step 4.3.1
Combine and .
Step 4.3.2
Combine and .
Step 4.3.3
Move to the left of .
Step 4.3.4
Cancel the common factor of and .
Step 4.3.4.1
Factor out of .
Step 4.3.4.2
Cancel the common factors.
Step 4.3.4.2.1
Raise to the power of .
Step 4.3.4.2.2
Factor out of .
Step 4.3.4.2.3
Cancel the common factor.
Step 4.3.4.2.4
Rewrite the expression.
Step 4.3.4.2.5
Divide by .
Step 4.3.5
Combine and .
Step 4.3.6
Combine and .
Step 4.3.7
Move to the left of .
Step 4.3.8
Cancel the common factor of and .
Step 4.3.8.1
Factor out of .
Step 4.3.8.2
Cancel the common factors.
Step 4.3.8.2.1
Raise to the power of .
Step 4.3.8.2.2
Factor out of .
Step 4.3.8.2.3
Cancel the common factor.
Step 4.3.8.2.4
Rewrite the expression.
Step 4.3.8.2.5
Divide by .
Step 4.3.9
Combine and .
Step 4.3.10
Combine and .
Step 4.3.11
Move to the left of .
Step 4.3.12
Cancel the common factor of .
Step 4.3.12.1
Cancel the common factor.
Step 4.3.12.2
Divide by .
Step 4.3.13
Move to the left of .
Step 4.4
Reorder terms.