Find the Derivative – d/dx natural log of xe^(-2x)

Math
Differentiate using the chain rule, which states that is where and .
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To apply the Chain Rule, set as .
The derivative of with respect to is .
Replace all occurrences of with .
Differentiate using the Product Rule which states that is where and .
Differentiate using the chain rule, which states that is where and .
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To apply the Chain Rule, set as .
Differentiate using the Exponential Rule which states that is where =.
Replace all occurrences of with .
Differentiate.
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Since is constant with respect to , the derivative of with respect to is .
Move to the left of .
Differentiate using the Power Rule which states that is where .
Multiply by .
Differentiate using the Power Rule which states that is where .
Multiply by .
Simplify.
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Apply the distributive property.
Combine terms.
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Combine and .
Combine and .
Combine and .
Move to the left of .
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Combine and .
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Reorder terms.
Find the Derivative – d/dx natural log of xe^(-2x)

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