Calculus Examples

Find the Derivative - d/dx ((sin(x))/(1+cos(x)))^2
Step 1
Differentiate using the chain rule, which states that is where and .
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Step 1.1
To apply the Chain Rule, set as .
Step 1.2
Differentiate using the Power Rule which states that is where .
Step 1.3
Replace all occurrences of with .
Step 2
Combine and .
Step 3
Differentiate using the Quotient Rule which states that is where and .
Step 4
The derivative of with respect to is .
Step 5
Differentiate.
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Step 5.1
By the Sum Rule, the derivative of with respect to is .
Step 5.2
Since is constant with respect to , the derivative of with respect to is .
Step 5.3
Add and .
Step 6
The derivative of with respect to is .
Step 7
Multiply.
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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
Multiply by .
Step 13
Multiply by by adding the exponents.
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Step 13.1
Multiply by .
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Step 13.1.1
Raise to the power of .
Step 13.1.2
Use the power rule to combine exponents.
Step 13.2
Add and .
Step 14
Simplify.
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Step 14.1
Apply the distributive property.
Step 14.2
Apply the distributive property.
Step 14.3
Simplify each term.
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Step 14.3.1
Reorder and .
Step 14.3.2
Multiply by .
Step 14.3.3
Apply the sine double-angle identity.
Step 14.3.4
Apply the sine double-angle identity.
Step 14.3.5
Multiply by by adding the exponents.
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Step 14.3.5.1
Move .
Step 14.3.5.2
Multiply by .
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Step 14.3.5.2.1
Raise to the power of .
Step 14.3.5.2.2
Use the power rule to combine exponents.
Step 14.3.5.3
Add and .
Step 14.4
Reorder terms.