NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.5 Question 12

✅ Step-by-Step Solution

1. Use logarithmic/chain differentiation of each variable power. Work with x,y>0 for the real variable powers.
2. Differentiating with respect to x gives \(y^{x} \log{\left(y \right)} + \frac{x^{y} y}{x}\) + \(\frac{x y^{x}}{y} + x^{y} \log{\left(x \right)}\) y′=0.
3. Collect y′ terms and divide by \(\frac{x y^{x}}{y} + x^{y} \log{\left(x \right)}\) when nonzero: y′=\(- \frac{y \left(x y^{x} \log{\left(y \right)} + x^{y} y\right)}{x \left(x y^{x} + x^{y} y \log{\left(x \right)}\right)}\).