Find the 3rd Derivative xe^x

Math
Find the first derivative.
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Differentiate using the Product Rule which states that is where and .
Differentiate using the Exponential Rule which states that is where =.
Differentiate using the Power Rule.
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Differentiate using the Power Rule which states that is where .
Simplify the expression.
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Multiply by .
Reorder terms.
Find the second derivative.
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By the Sum Rule, the derivative of with respect to is .
Evaluate .
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Differentiate using the Product Rule which states that is where and .
Differentiate using the Power Rule which states that is where .
Differentiate using the Exponential Rule which states that is where =.
Multiply by .
Differentiate using the Exponential Rule which states that is where =.
Simplify.
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Add and .
Reorder terms.
Find the third derivative.
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By the Sum Rule, the derivative of with respect to is .
Evaluate .
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Differentiate using the Product Rule which states that is where and .
Differentiate using the Power Rule which states that is where .
Differentiate using the Exponential Rule which states that is where =.
Multiply by .
Evaluate .
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Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Exponential Rule which states that is where =.
Simplify.
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Add and .
Reorder terms.
Find the fourth derivative.
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By the Sum Rule, the derivative of with respect to is .
Evaluate .
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Differentiate using the Product Rule which states that is where and .
Differentiate using the Power Rule which states that is where .
Differentiate using the Exponential Rule which states that is where =.
Multiply by .
Evaluate .
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Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Exponential Rule which states that is where =.
Simplify.
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Add and .
Reorder terms.
Find the 3rd Derivative xe^x

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