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CBSE Class 12 Math 2022 Term I Solved Paper

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In this section, attempt any 16 questions out of Questions 1-20. Each question is of one mark.
1. Differential of log⁡[log⁡(log⁡x5)]\log \left[ \log \left( \log x^5 \right) \right] w.r.t xx is
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Explanation: Let
∴    ddx=1log⁡(log⁡x5)ddx[log⁡(log⁡x5)]\therefore \;\; \frac{d}{dx} = \frac{1}{\log \left( \log x^5 \right)} \frac{d}{dx} \left[ \log \left( \log x^5 \right) \right]
=1log⁡(log⁡x5)⋅1log⁡x5ddxlog⁡x5= \frac{1}{\log \left( \log x^5 \right)} \cdot \frac{1}{\log x^5} \frac{d}{dx} \log x^5
=1log⁡(x5)log⁡(log⁡x5)1x5ddx(x5)= \frac{1}{\log \left( x^5 \right) \log \left( \log x^5 \right)} \frac{1}{x^5} \frac{d}{dx} (x^5)
=5xlog⁡(x5)log⁡(log⁡x5)= \frac{5}{x \log \left( x^5 \right) \log \left( \log x^5 \right)}
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