==> $\log y = \log \log x[\log x + \log \log x]$
==> $\frac{1}{y}\frac{{dy}}{{dx}} = \frac{1}{{x\log x}}(\log x + \log \log x) + \log \log x\left( {\frac{1}{x} + \frac{1}{{x\log x}}} \right)$
==> $\frac{{dy}}{{dx}} = y\{ \frac{1}{{x\log x}}(\log x + \log \log x) + \log \log x\left( {\frac{1}{x} + \frac{1}{{x\log x}}} \right)\} $
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
| List $I$ | List $II$ |
| $P.\quad$ Volume of parallelopiped determined by vectors $\vec{a}, \vec{b}$ and $\overrightarrow{ c }$ is $2$ . Then the volume of the parallelepiped determined by vectors $2(\vec{a} \times \vec{b}), 3(\vec{b} \times \vec{c})$ and $(\vec{c} \times \vec{a})$ is | $1.\quad$ $100$ |
| $Q.\quad$ Volume of parallelepiped determined by vectors $\vec{a}, \vec{b}$ and $\vec{c}$ is $5$ . Then the volume of the parallelepiped determined by vectors $3(\overrightarrow{ a }+\overrightarrow{ b }),(\overrightarrow{ b }+\overrightarrow{ c })$ and $2(\overrightarrow{ c }+\overrightarrow{ a })$ is | $2.\quad$ $30$ |
| $R.\quad$ Area of a triangle with adjacent sides determined by vectors $\vec{a}$ and $\vec{b}$ is $20$ . Then the area of the triangle with adjacent sides determined by vectors $(2 \vec{a}+3 \vec{b})$ and $(\vec{a}-\vec{b})$ is | $3.\quad$ $24$ |
| $S.\quad$ Area of a paralelogram with adjacent sides determined by vectors $\vec{a}$ and $\vec{b}$ is $30$ . Then the area of the parallelogram with adjacent sides determined by vectors $(\vec{a}+\vec{b})$ and $\vec{a}$ is | $4.\quad$ $60$ |
Codes: $ \quad P \quad Q \quad R \quad S $