Calculus Examples

Find the Derivative - d/dx y=3(sin(x)+cos(x))(sin(x)-cos(x))
Step 1
Since is constant with respect to , the derivative of with respect to is .
Step 2
Differentiate using the Product Rule which states that is where and .
Step 3
By the Sum Rule, the derivative of with respect to is .
Step 4
The derivative of with respect to is .
Step 5
Since is constant with respect to , the derivative of with respect to is .
Step 6
The derivative of with respect to is .
Step 7
Differentiate using the Sum Rule.
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Step 7.1
Multiply by .
Step 7.2
Multiply by .
Step 7.3
By the Sum Rule, the derivative of with respect to is .
Step 8
The derivative of with respect to is .
Step 9
The derivative of with respect to is .
Step 10
Simplify.
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Step 10.1
Apply the distributive property.
Step 10.2
Remove parentheses.
Step 10.3
Reorder terms.
Step 10.4
Simplify each term.
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Step 10.4.1
Apply the distributive property.
Step 10.4.2
Expand using the FOIL Method.
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Step 10.4.2.1
Apply the distributive property.
Step 10.4.2.2
Apply the distributive property.
Step 10.4.2.3
Apply the distributive property.
Step 10.4.3
Simplify and combine like terms.
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Step 10.4.3.1
Simplify each term.
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Step 10.4.3.1.1
Multiply .
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Step 10.4.3.1.1.1
Raise to the power of .
Step 10.4.3.1.1.2
Raise to the power of .
Step 10.4.3.1.1.3
Use the power rule to combine exponents.
Step 10.4.3.1.1.4
Add and .
Step 10.4.3.1.2
Multiply .
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Step 10.4.3.1.2.1
Raise to the power of .
Step 10.4.3.1.2.2
Raise to the power of .
Step 10.4.3.1.2.3
Use the power rule to combine exponents.
Step 10.4.3.1.2.4
Add and .
Step 10.4.3.2
Reorder the factors of .
Step 10.4.3.3
Add and .
Step 10.4.4
Factor out of .
Step 10.4.5
Factor out of .
Step 10.4.6
Factor out of .
Step 10.4.7
Rearrange terms.
Step 10.4.8
Apply pythagorean identity.
Step 10.4.9
Multiply by .
Step 10.4.10
Apply the distributive property.
Step 10.4.11
Multiply by .
Step 10.4.12
Expand using the FOIL Method.
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Step 10.4.12.1
Apply the distributive property.
Step 10.4.12.2
Apply the distributive property.
Step 10.4.12.3
Apply the distributive property.
Step 10.4.13
Simplify and combine like terms.
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Step 10.4.13.1
Simplify each term.
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Step 10.4.13.1.1
Multiply .
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Step 10.4.13.1.1.1
Multiply by .
Step 10.4.13.1.1.2
Raise to the power of .
Step 10.4.13.1.1.3
Raise to the power of .
Step 10.4.13.1.1.4
Use the power rule to combine exponents.
Step 10.4.13.1.1.5
Add and .
Step 10.4.13.1.2
Multiply .
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Step 10.4.13.1.2.1
Raise to the power of .
Step 10.4.13.1.2.2
Raise to the power of .
Step 10.4.13.1.2.3
Use the power rule to combine exponents.
Step 10.4.13.1.2.4
Add and .
Step 10.4.13.1.3
Multiply by .
Step 10.4.13.2
Reorder the factors of .
Step 10.4.13.3
Add and .
Step 10.4.14
Factor out of .
Step 10.4.15
Factor out of .
Step 10.4.16
Factor out of .
Step 10.4.17
Rearrange terms.
Step 10.4.18
Apply pythagorean identity.
Step 10.4.19
Multiply by .
Step 10.5
Combine the opposite terms in .
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Step 10.5.1
Subtract from .
Step 10.5.2
Add and .
Step 10.6
Add and .