CUET · MATHS · PYQ PAPER 2023
The derivative of \(\sqrt{e^{\sqrt{x}}}\) with respect to \(x\) is :
- A \(\frac{\sqrt{e^{\sqrt{x}}}}{2 \sqrt{x}}\)
- B \(\frac{e^{\sqrt{x}}}{4 \sqrt{x}}\)
- C \(\frac{\sqrt{e^{\sqrt{x}}}}{4 \sqrt{x}}\)
- D \(\frac{e^{\sqrt{x}}}{2 \sqrt{x}}\)
Answer & Solution
Correct Answer
(C) \(\frac{\sqrt{e^{\sqrt{x}}}}{4 \sqrt{x}}\)
Step-by-step Solution
Detailed explanation
\(y = \sqrt{e^{\sqrt{x}}} = e^{\frac{1}{2}\sqrt{x}}\) \(\frac{dy}{dx} = e^{\frac{1}{2}\sqrt{x}} \cdot \frac{d}{dx}\left(\frac{1}{2}\sqrt{x}\right)\) \(\frac{dy}{dx} = e^{\frac{1}{2}\sqrt{x}} \cdot \frac{1}{2} \cdot \frac{1}{2\sqrt{x}}\)…
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