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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
Differentiate using the Exponential Rule which states that is where =.
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 5
Step 5.1
To apply the Chain Rule, set as .
Step 5.2
Differentiate using the Exponential Rule which states that is where =.
Step 5.3
Replace all occurrences of with .
Step 6
Step 6.1
Since is constant with respect to , the derivative of with respect to is .
Step 6.2
Differentiate using the Power Rule which states that is where .
Step 6.3
Simplify the expression.
Step 6.3.1
Multiply by .
Step 6.3.2
Move to the left of .
Step 6.4
Differentiate using the Power Rule which states that is where .
Step 6.5
Multiply by .
Step 7
Step 7.1
Apply the distributive property.
Step 7.2
Apply the distributive property.
Step 7.3
Simplify each term.
Step 7.3.1
Rewrite using the commutative property of multiplication.
Step 7.3.2
Rewrite using the commutative property of multiplication.
Step 7.4
Reorder terms.
Step 7.5
Reorder factors in .