y=x^2lnx হলে y_3 নির্ণয় কর 

দেওয়া আছে, \(y = x^2 \ln x\)

প্রথম অন্তরকলন, \(y_1 = \frac{dy}{dx}\)

\(y_1 = \frac{d}{dx}(x^2 \ln x) = x^2 \cdot \frac{1}{x} + \ln x \cdot 2x = x + 2x \ln x\)

দ্বিতীয় অন্তরকলন, \(y_2 = \frac{d^2y}{dx^2} = \frac{dy_1}{dx}\)

\(y_2 = \frac{d}{dx}(x + 2x \ln x) = 1 + 2(x \cdot \frac{1}{x} + \ln x \cdot 1) = 1 + 2(1 + \ln x) = 3 + 2 \ln x\)

তৃতীয় অন্তরকলন, \(y_3 = \frac{d^3y}{dx^3} = \frac{dy_2}{dx}\)

\(y_3 = \frac{d}{dx}(3 + 2 \ln x) = 0 + 2 \cdot \frac{1}{x} = \frac{2}{x}\)

অতএব, \(y_3 = \frac{2}{x}\) 🎉