Final answer:
To find the derivative of y = x^2x using logarithmic differentiation, take the natural logarithm of both sides of the equation and apply differentiation rules, including the product rule and chain rule.
Step-by-step explanation:
To find the derivative of y = x2x using logarithmic differentiation, we can take the natural logarithm of both sides of the equation. This allows us to simplify the expression and apply differentiation rules.
Starting with y = x2x, we take the natural logarithm of both sides: ln(y) = ln(x2x).
Next, we can use logarithmic properties to simplify the expression. Applying the power rule of logarithms, we get: ln(y) = (2x)ln(x).
Now, we can differentiate both sides of the equation with respect to x. The derivative of ln(y) is 1/y(dy/dx), and the derivative of (2x)ln(x) can be found using the product rule and chain rule. Simplifying the expression, we get the derivative of y = x2x.