Calculus Examples

Find the Derivative - d/dx y=x^2e^x-2xe^x+2e^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
Differentiate using the Exponential Rule which states that is where =.
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
Differentiate using the Exponential Rule which states that is where =.
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
Differentiate using the Exponential Rule which states that is where =.
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
Subtract from .
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Step 5.2.1.1
Move .
Step 5.2.1.2
Subtract from .
Step 5.2.2
Add and .
Step 5.2.3
Add and .
Step 5.2.4
Add and .
Step 5.3
Reorder the factors of .
Step 5.4
Reorder factors in .