NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Miscellaneous Exercise Question 3

✅ Step-by-Step Solution

1. Work for x>0.
2. For a positive base u, write uᵛ=exp(v log u). Its derivative is uᵛ(v′ log u+vu′/u). Here \(\frac{d}{d x} \left(5 x\right)^{3 \cos{\left(2 x \right)}}\) = \(\left(5 x\right)^{3 \cos{\left(2 x \right)}} \left(- 6 \log{\left(5 x \right)} \sin{\left(2 x \right)} + \frac{3 \cos{\left(2 x \right)}}{x}\right)\).
3. Combining the terms gives y′ = \(\left(5 x\right)^{3 \cos{\left(2 x \right)}} \left(- 6 \log{\left(5 x \right)} \sin{\left(2 x \right)} + \frac{3 \cos{\left(2 x \right)}}{x}\right)\).