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Calculus Examples
Step 1
Since is constant with respect to , the derivative of with respect to is .
Step 2
Differentiate using the Quotient Rule which states that is where and .
Step 3
Differentiate using the Product Rule which states that is where and .
Step 4
The derivative of with respect to is .
Step 5
Step 5.1
Differentiate using the Power Rule which states that is where .
Step 5.2
Multiply by .
Step 5.3
By the Sum Rule, the derivative of with respect to is .
Step 5.4
Since is constant with respect to , the derivative of with respect to is .
Step 5.5
Add and .
Step 6
The derivative of with respect to is .
Step 7
Step 7.1
Multiply by .
Step 7.2
Multiply by .
Step 8
Raise to the power of .
Step 9
Raise to the power of .
Step 10
Use the power rule to combine exponents.
Step 11
Add and .
Step 12
Combine and .
Step 13
Step 13.1
Apply the distributive property.
Step 13.2
Simplify the numerator.
Step 13.2.1
Simplify each term.
Step 13.2.1.1
Expand using the FOIL Method.
Step 13.2.1.1.1
Apply the distributive property.
Step 13.2.1.1.2
Apply the distributive property.
Step 13.2.1.1.3
Apply the distributive property.
Step 13.2.1.2
Simplify each term.
Step 13.2.1.2.1
Multiply by .
Step 13.2.1.2.2
Multiply by .
Step 13.2.1.2.3
Multiply .
Step 13.2.1.2.3.1
Raise to the power of .
Step 13.2.1.2.3.2
Raise to the power of .
Step 13.2.1.2.3.3
Use the power rule to combine exponents.
Step 13.2.1.2.3.4
Add and .
Step 13.2.1.3
Apply the distributive property.
Step 13.2.1.4
Simplify.
Step 13.2.1.4.1
Reorder and .
Step 13.2.1.4.2
Reorder and .
Step 13.2.1.4.3
Apply the sine double-angle identity.
Step 13.2.2
Move .
Step 13.2.3
Factor out of .
Step 13.2.4
Factor out of .
Step 13.2.5
Factor out of .
Step 13.2.6
Rearrange terms.
Step 13.2.7
Apply pythagorean identity.
Step 13.2.8
Multiply by .
Step 13.3
Reorder terms.