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Calculus Examples
Step 1
Differentiate using the Quotient Rule which states that is where and .
Step 2
Differentiate using the Product Rule which states that is where and .
Step 3
The derivative of with respect to is .
Step 4
Step 4.1
Differentiate using the Power Rule which states that is where .
Step 4.2
Multiply by .
Step 4.3
By the Sum Rule, the derivative of with respect to is .
Step 4.4
Since is constant with respect to , the derivative of with respect to is .
Step 4.5
Add and .
Step 5
The derivative of with respect to is .
Step 6
Step 6.1
Multiply by .
Step 6.2
Multiply by .
Step 7
Raise to the power of .
Step 8
Raise to the power of .
Step 9
Use the power rule to combine exponents.
Step 10
Add and .
Step 11
Step 11.1
Simplify the numerator.
Step 11.1.1
Simplify each term.
Step 11.1.1.1
Expand using the FOIL Method.
Step 11.1.1.1.1
Apply the distributive property.
Step 11.1.1.1.2
Apply the distributive property.
Step 11.1.1.1.3
Apply the distributive property.
Step 11.1.1.2
Multiply .
Step 11.1.1.2.1
Raise to the power of .
Step 11.1.1.2.2
Raise to the power of .
Step 11.1.1.2.3
Use the power rule to combine exponents.
Step 11.1.1.2.4
Add and .
Step 11.1.2
Move .
Step 11.1.3
Factor out of .
Step 11.1.4
Factor out of .
Step 11.1.5
Factor out of .
Step 11.1.6
Rearrange terms.
Step 11.1.7
Apply pythagorean identity.
Step 11.1.8
Multiply by .
Step 11.2
Reorder terms.