Calculus Examples

Find dy/dx y=sin(x)cos(x)
Step 1
Differentiate both sides of the equation.
Step 2
The derivative of with respect to is .
Step 3
Differentiate the right side of the equation.
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Step 3.1
Differentiate using the Product Rule which states that is where and .
Step 3.2
The derivative of with respect to is .
Step 3.3
Raise to the power of .
Step 3.4
Raise to the power of .
Step 3.5
Use the power rule to combine exponents.
Step 3.6
Add and .
Step 3.7
The derivative of with respect to is .
Step 3.8
Raise to the power of .
Step 3.9
Raise to the power of .
Step 3.10
Use the power rule to combine exponents.
Step 3.11
Add and .
Step 3.12
Simplify.
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Step 3.12.1
Reorder and .
Step 3.12.2
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 3.12.3
Expand using the FOIL Method.
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Step 3.12.3.1
Apply the distributive property.
Step 3.12.3.2
Apply the distributive property.
Step 3.12.3.3
Apply the distributive property.
Step 3.12.4
Combine the opposite terms in .
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Step 3.12.4.1
Reorder the factors in the terms and .
Step 3.12.4.2
Add and .
Step 3.12.4.3
Add and .
Step 3.12.5
Simplify each term.
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Step 3.12.5.1
Multiply .
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Step 3.12.5.1.1
Raise to the power of .
Step 3.12.5.1.2
Raise to the power of .
Step 3.12.5.1.3
Use the power rule to combine exponents.
Step 3.12.5.1.4
Add and .
Step 3.12.5.2
Rewrite using the commutative property of multiplication.
Step 3.12.5.3
Multiply .
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Step 3.12.5.3.1
Raise to the power of .
Step 3.12.5.3.2
Raise to the power of .
Step 3.12.5.3.3
Use the power rule to combine exponents.
Step 3.12.5.3.4
Add and .
Step 3.12.6
Apply the cosine double-angle identity.
Step 4
Reform the equation by setting the left side equal to the right side.
Step 5
Replace with .