What is dy/dx for this y = x^x?

Question 90

MediumOriginal question

Let $y = x^{x}$ for $x > 0$ .

What is $\frac{dy}{dx}$ for this $y = x^{x}$ ?

x^{x}(1 + \log x)

Correct answerYour answer

x \cdot x^{x - 1}

Correct answerYour answer

x^{x}\log x

Correct answerYour answer

1 + \log x

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Worth noting

$1 + \log x$ is $\frac{1}{y}\frac{dy}{dx}$ , before multiplying back by $y$ .

Ten questions from Chain Rule, Log Differentiation & Rate of Change, at your own pace.

Ten questions from Chain Rule, Log Differentiation & Rate of Change, at your own pace.