NCERT Class 12 · Ch 5 Exercise 5.4 · Q7
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.4 Question 7
Differentiate \(e^{\frac{\sqrt{x}}{2}}\) 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: \(\frac{e^{\frac{\sqrt{x}}{2}}}{4 \sqrt{x}}\)
- Work for x>0.
- Differentiate the outer function and multiply by the inner derivative: \(\frac{d}{d x} e^{\frac{\sqrt{x}}{2}}\) = \(\frac{e^{\frac{\sqrt{x}}{2}}}{4 \sqrt{x}}\).
- Combining the terms gives y′ = \(\frac{e^{\frac{\sqrt{x}}{2}}}{4 \sqrt{x}}\).
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