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Calculus Examples
Step 1
Step 1.1
To apply the Chain Rule, set as .
Step 1.2
The derivative of with respect to is .
Step 1.3
Replace all occurrences of with .
Step 2
Combine and .
Step 3
Multiply by the reciprocal of the fraction to divide by .
Step 4
Multiply by .
Step 5
Differentiate using the Quotient Rule which states that is where and .
Step 6
Step 6.1
By the Sum Rule, the derivative of with respect to is .
Step 6.2
Differentiate using the Power Rule which states that is where .
Step 6.3
Since is constant with respect to , the derivative of with respect to is .
Step 6.4
Simplify the expression.
Step 6.4.1
Add and .
Step 6.4.2
Move to the left of .
Step 6.5
By the Sum Rule, the derivative of with respect to is .
Step 6.6
Differentiate using the Power Rule which states that is where .
Step 6.7
Since is constant with respect to , the derivative of with respect to is .
Step 6.8
Combine fractions.
Step 6.8.1
Add and .
Step 6.8.2
Multiply by .
Step 6.8.3
Multiply by .
Step 7
Step 7.1
Factor out of .
Step 7.2
Cancel the common factor.
Step 7.3
Rewrite the expression.
Step 8
Step 8.1
Apply the distributive property.
Step 8.2
Apply the distributive property.
Step 8.3
Apply the distributive property.
Step 8.4
Apply the distributive property.
Step 8.5
Simplify the numerator.
Step 8.5.1
Simplify each term.
Step 8.5.1.1
Multiply by by adding the exponents.
Step 8.5.1.1.1
Move .
Step 8.5.1.1.2
Multiply by .
Step 8.5.1.2
Multiply by .
Step 8.5.1.3
Multiply by .
Step 8.5.2
Subtract from .
Step 8.6
Reorder terms.