Question

If y = `x^(x^2)`, then `dy/dx` is equal to ______.

Options

• (2 ln x)

• (2 ln x + 1)

• `(ln ln x + 1)x^(x^2)`

• None of these

Answer 1

If y = `x^(x^2)`, then `dy/dx` is equal to none of these.

Explanation:

y = `x^(x^2)`, ln y = x² ln x

`1/y dy/dx = 2x ln x + x^2. 1/x` = x (l + 2 ln x)

`dy/dx = x^(x^2). x(1 + 2 ln x) = x^(x^2 + 1)(1 + 2 ln x)`