y=x^2lnx   হলে  (d^3y)/(dx^3)=  কত?  

Explanation:

Another Explanation (5): দেওয়া আছে, \(y = x^2 \ln x\) প্রথম অন্তরকলন, \[ \frac{dy}{dx} = \frac{d}{dx} (x^2 \ln x) = x^2 \cdot \frac{1}{x} + \ln x \cdot 2x = x + 2x \ln x \] 🤔 দ্বিতীয় অন্তরকলন, \[ \frac{d^2y}{dx^2} = \frac{d}{dx} (x + 2x \ln x) = 1 + 2(x \cdot \frac{1}{x} + \ln x \cdot 1) = 1 + 2(1 + \ln x) = 3 + 2 \ln x \] 😮 তৃতীয় অন্তরকলন, \[ \frac{d^3y}{dx^3} = \frac{d}{dx} (3 + 2 \ln x) = 0 + 2 \cdot \frac{1}{x} = \frac{2}{x} \] 😊 অতএব, \(\frac{d^3y}{dx^3} = \frac{2}{x}\)