NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.5 Question 14

✅ Step-by-Step Solution

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