NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.2 Question 5

✅ Step-by-Step Solution

1. Work where the denominator cos(cx+d) is nonzero.
2. Product rule: differentiate each variable factor once, keeping the other factors unchanged. Here \(\frac{\partial}{\partial x} \frac{\sin{\left(a x + b \right)}}{\cos{\left(c x + d \right)}}\) = \(\frac{a \cos{\left(a x + b \right)}}{\cos{\left(c x + d \right)}} + \frac{c \sin{\left(a x + b \right)} \sin{\left(c x + d \right)}}{\cos^{2}{\left(c x + d \right)}}\).
3. Combining the terms gives y′ = \(\frac{a \cos{\left(a x + b \right)} + \frac{c \sin{\left(a x + b \right)} \sin{\left(c x + d \right)}}{\cos{\left(c x + d \right)}}}{\cos{\left(c x + d \right)}}\).