যদি xⁿ + yⁿ = aⁿ হয় তবে   (dy)/(dx)=? 

Explanation:

Another Explanation (5): দেওয়া আছে, \(x^n + y^n = a^n\) উভয়পক্ষে \(x\) এর সাপেক্ষে অন্তরকলন করে পাই, \(\frac{d}{dx}(x^n + y^n) = \frac{d}{dx}(a^n)\) \(\implies \frac{d}{dx}(x^n) + \frac{d}{dx}(y^n) = 0\) (\(\because a\) ধ্রুবক) \(\implies nx^{n-1} + ny^{n-1}\frac{dy}{dx} = 0\) (\(\because\) এখানে \(y, x\) এর ফাংশন) \(\implies ny^{n-1}\frac{dy}{dx} = -nx^{n-1}\) \(\implies \frac{dy}{dx} = \frac{-nx^{n-1}}{ny^{n-1}}\) \(\implies \frac{dy}{dx} = -\frac{x^{n-1}}{y^{n-1}}\) \(\implies \frac{dy}{dx} = -(\frac{x}{y})^{n-1}\) সুতরাং, \(\frac{dy}{dx} = -(\frac{x}{y})^{n-1}\) 🥳