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Calculus Examples
Step 1
Differentiate using the Quotient Rule which states that is where and .
Step 2
By the Sum Rule, the derivative of with respect to is .
Step 3
Step 3.1
To apply the Chain Rule, set as .
Step 3.2
The derivative of with respect to is .
Step 3.3
Replace all occurrences of with .
Step 4
Step 4.1
Since is constant with respect to , the derivative of with respect to is .
Step 4.2
Differentiate using the Power Rule which states that is where .
Step 4.3
Simplify the expression.
Step 4.3.1
Multiply by .
Step 4.3.2
Move to the left of .
Step 4.4
Since is constant with respect to , the derivative of with respect to is .
Step 5
Differentiate using the Exponential Rule which states that is where =.
Step 6
Step 6.1
By the Sum Rule, the derivative of with respect to is .
Step 6.2
Since is constant with respect to , the derivative of with respect to is .
Step 6.3
Differentiate using the Power Rule which states that is where .
Step 6.4
Multiply by .
Step 6.5
Since is constant with respect to , the derivative of with respect to is .
Step 6.6
Simplify the expression.
Step 6.6.1
Add and .
Step 6.6.2
Multiply by .
Step 7
Step 7.1
Apply the distributive property.
Step 7.2
Simplify the numerator.
Step 7.2.1
Simplify each term.
Step 7.2.1.1
Expand using the FOIL Method.
Step 7.2.1.1.1
Apply the distributive property.
Step 7.2.1.1.2
Apply the distributive property.
Step 7.2.1.1.3
Apply the distributive property.
Step 7.2.1.2
Simplify each term.
Step 7.2.1.2.1
Rewrite using the commutative property of multiplication.
Step 7.2.1.2.2
Multiply by .
Step 7.2.1.2.3
Rewrite using the commutative property of multiplication.
Step 7.2.1.2.4
Multiply by .
Step 7.2.1.2.5
Multiply by .
Step 7.2.1.2.6
Multiply by .
Step 7.2.1.3
Multiply by .
Step 7.2.2
Add and .
Step 7.3
Reorder terms.