Calculus Examples

Find the Derivative - d/dx y=(2xsin(x))/(1+cos(x))
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
Differentiate.
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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
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
Combine and .
Step 13
Simplify.
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Step 13.1
Apply the distributive property.
Step 13.2
Simplify the numerator.
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Step 13.2.1
Simplify each term.
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Step 13.2.1.1
Expand using the FOIL Method.
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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.
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Step 13.2.1.2.1
Multiply by .
Step 13.2.1.2.2
Multiply by .
Step 13.2.1.2.3
Multiply .
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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.
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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.