Question

Find(dy/dx) by logarithmic differentiation for the function (y = x^(ln(x))

Answer 1

To find dy/dx for the function y = x^(ln(x)), you can use logarithmic differentiation. The derivative is (2ln(x)y)/x.

Step-by-step explanation:

To find ∫y/∫x for the function y = x^(ln(x)), we can use logarithmic differentiation. Let's go step by step:

1. Take the natural logarithm of both sides of the equation: ln(y) = ln(x^(ln(x))).
2. Apply the power rule of logarithms to simplify the equation: ln(y) = (ln(x))(ln(x)).
3. Differentiate both sides with respect to x: 1/y * dy/dx = (2ln(x))/x.
4. Solve for dy/dx by multiplying both sides by y: dy/dx = (2ln(x)y)/x.

So, the derivative of y = x^(ln(x)) with respect to x is dy/dx = (2ln(x)y)/x.