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Calculus Examples
Step 1
Differentiate using the Quotient Rule which states that is where and .
Step 2
Step 2.1
To apply the Chain Rule, set as .
Step 2.2
The derivative of with respect to is .
Step 2.3
Replace all occurrences of with .
Step 3
Step 3.1
Since is constant with respect to , the derivative of with respect to is .
Step 3.2
Differentiate using the Power Rule which states that is where .
Step 3.3
Simplify the expression.
Step 3.3.1
Multiply by .
Step 3.3.2
Move to the left of .
Step 3.4
By the Sum Rule, the derivative of with respect to is .
Step 3.5
Since is constant with respect to , the derivative of with respect to is .
Step 3.6
Add and .
Step 4
Step 4.1
To apply the Chain Rule, set as .
Step 4.2
The derivative of with respect to is .
Step 4.3
Replace all occurrences of with .
Step 5
Raise to the power of .
Step 6
Use the power rule to combine exponents.
Step 7
Add and .
Step 8
Since is constant with respect to , the derivative of with respect to is .
Step 9
Multiply by .
Step 10
Differentiate using the Power Rule which states that is where .
Step 11
Multiply by .
Step 12
Step 12.1
Apply the distributive property.
Step 12.2
Apply the distributive property.
Step 12.3
Apply the distributive property.
Step 12.4
Simplify the numerator.
Step 12.4.1
Simplify each term.
Step 12.4.1.1
Multiply by .
Step 12.4.1.2
Multiply .
Step 12.4.1.2.1
Raise to the power of .
Step 12.4.1.2.2
Raise to the power of .
Step 12.4.1.2.3
Use the power rule to combine exponents.
Step 12.4.1.2.4
Add and .
Step 12.4.2
Factor out of .
Step 12.4.2.1
Factor out of .
Step 12.4.2.2
Factor out of .
Step 12.4.2.3
Factor out of .
Step 12.4.2.4
Factor out of .
Step 12.4.2.5
Factor out of .
Step 12.4.3
Reorder and .
Step 12.4.4
Factor out of .
Step 12.4.5
Factor out of .
Step 12.4.6
Factor out of .
Step 12.4.7
Apply pythagorean identity.
Step 12.4.8
Multiply by .
Step 12.4.9
Apply the distributive property.
Step 12.4.10
Multiply by .
Step 12.5
Factor out of .
Step 12.5.1
Factor out of .
Step 12.5.2
Factor out of .
Step 12.5.3
Factor out of .