Question

Differentiate x ^ { x } with respect to x​

Answer 1

To solve this, we need the knowledge of the Product Rule, the Chain Rule and Implicit Differentiation.

$y=x^x\\\\ln(y)=ln(x^x)\\\\ln(y)=x*ln(x)\\\\\frac{d}{dx}(ln(y))=\frac{d}{dx}(x*ln(x))\\\\\frac{1}{y}*\frac{dy}{dx} = 1*ln(x)+x*\frac{1}{x}\\\\\frac{dy}{dx} =y*(ln(x)+1)\\\\\frac{dy}{dx} =x^x*(ln(x)+1)$

Answer 2

Ur answer....yaar

Step-by-step explanation:

To solve this, we need the knowledge of the Product Rule, the Chain Rule and Implicit Differentiation.

$y=x^x\\\\ln(y)=ln(x^x)\\\\ln(y)=x*ln(x)\\\\\frac{d}{dx}(ln(y))=\frac{d}{dx}(x*ln(x))\\\\\frac{1}{y}*\frac{dy}{dx} = 1*ln(x)+x*\frac{1}{x}\\\\\frac{dy}{dx} =y*(ln(x)+1)\\\\\frac{dy}{dx} =x^x*(ln(x)+1)$