NCERT Class 12 · Ch 5 Exercise 5.4 · Q10
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.4 Question 10
Differentiate \(\cos{\left(e^{x} + \log{\left(x \right)} \right)}\) with respect to x; for x>0.
💡 Concept Hints
- Identify the domain and the inner and outer functions, or the relevant one-sided limits.
- Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.
✅ Step-by-Step Solution
Final Answer: \(- \left(e^{x} + \frac{1}{x}\right) \sin{\left(e^{x} + \log{\left(x \right)} \right)}\)
- Work for x>0.
- Differentiate the outer function and multiply by the inner derivative: \(\frac{d}{d x} \cos{\left(e^{x} + \log{\left(x \right)} \right)}\) = \(- \left(e^{x} + \frac{1}{x}\right) \sin{\left(e^{x} + \log{\left(x \right)} \right)}\).
- Combining the terms gives y′ = \(- \left(e^{x} + \frac{1}{x}\right) \sin{\left(e^{x} + \log{\left(x \right)} \right)}\).
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