Calculus Examples

Find the Derivative - d/dx x^2sin(x)+2xcos(x)-2sin(x)
Step 1
By the Sum Rule, the derivative of with respect to is .
Step 2
Evaluate .
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Step 2.1
Differentiate using the Product Rule which states that is where and .
Step 2.2
The derivative of with respect to is .
Step 2.3
Differentiate using the Power Rule which states that is where .
Step 3
Evaluate .
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Step 3.1
Since is constant with respect to , the derivative of with respect to is .
Step 3.2
Differentiate using the Product Rule which states that is where and .
Step 3.3
The derivative of with respect to is .
Step 3.4
Differentiate using the Power Rule which states that is where .
Step 3.5
Multiply by .
Step 4
Evaluate .
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Step 4.1
Since is constant with respect to , the derivative of with respect to is .
Step 4.2
The derivative of with respect to is .
Step 5
Simplify.
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Step 5.1
Apply the distributive property.
Step 5.2
Combine terms.
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Step 5.2.1
Multiply by .
Step 5.2.2
Subtract from .
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Step 5.2.2.1
Move .
Step 5.2.2.2
Subtract from .
Step 5.2.3
Add and .
Step 5.2.4
Subtract from .
Step 5.2.5
Add and .