Use Logarithmic Differentiation to Find the Derivative y=x^(2x)

Math
Let , take the natural logarithm of both sides .
Expand by moving outside the logarithm.
Differentiate the expression using the chain rule, keeping in mind that is a function of .
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Differentiate the left hand side using the chain rule.
Differentiate the right hand side.
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Differentiate .
Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Product Rule which states that is where and .
The derivative of with respect to is .
Combine and .
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Differentiate using the Power Rule which states that is where .
Multiply by .
Simplify.
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Apply the distributive property.
Multiply by .
Reorder terms.
Isolate and substitute the original function for in the right hand side.
Simplify the right hand side.
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Simplify by moving inside the logarithm.
Apply the distributive property.
Reorder factors in .
Use Logarithmic Differentiation to Find the Derivative y=x^(2x)

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