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Calculus Examples
Step 1
Differentiate using the Quotient Rule which states that is where and .
Step 2
Step 2.1
By the Sum Rule, the derivative of with respect to is .
Step 2.2
Since is constant with respect to , the derivative of with respect to is .
Step 2.3
Add and .
Step 2.4
Since is constant with respect to , the derivative of with respect to is .
Step 3
The derivative of with respect to is .
Step 4
Step 4.1
Multiply by .
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
Apply the distributive property.
Step 6.2
Apply the distributive property.
Step 6.3
Apply the distributive property.
Step 6.4
Simplify the numerator.
Step 6.4.1
Simplify each term.
Step 6.4.1.1
Multiply .
Step 6.4.1.1.1
Raise to the power of .
Step 6.4.1.1.2
Raise to the power of .
Step 6.4.1.1.3
Use the power rule to combine exponents.
Step 6.4.1.1.4
Add and .
Step 6.4.1.2
Multiply by .
Step 6.4.1.3
Multiply .
Step 6.4.1.3.1
Multiply by .
Step 6.4.1.3.2
Multiply by .
Step 6.4.1.4
Multiply .
Step 6.4.1.4.1
Raise to the power of .
Step 6.4.1.4.2
Raise to the power of .
Step 6.4.1.4.3
Use the power rule to combine exponents.
Step 6.4.1.4.4
Add and .
Step 6.4.2
Move .
Step 6.4.3
Apply pythagorean identity.
Step 6.5
Reorder terms.