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explain solution RD Sharma class 12 chapter Differentiation exercise 10.2 question 24 maths

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Answer: \frac{e^{\sqrt{\cot x}} \times(\operatorname{cosec})^{2} x}{2 \sqrt{\cot x}}

Hint: You must know the rules of solving derivative of trigonometric and exponential function.

Given: e^{\sqrt{\cot x}}


Let  y=e^{\sqrt{\cot x}}

y=e^{(\cot x)^{\frac{1}{2}}}

Differentiate both sides

\frac{d y}{d x}=\frac{d}{d x} e^{(\cot x)^{\frac{1}{2}}}

Using Chain Rule,

\frac{d y}{d x}=e^{(\cot x)^{\frac{1}{2}}} \times \frac{1}{2}(\cot x)^{\frac{1}{2}-1} \frac{d}{d x}(\cot x)

\frac{d y}{d x}=\frac{e^{\sqrt{\cot x}} \times(\operatorname{cosec})^{2} x}{2 \sqrt{\cot x}}

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