Question
Differentiate the following function with respect to $(\text{x})$:
$\Big\{\log\Big(\frac{1}{\sqrt{\text{x}}}\Big)+5\text{x}^\text{a}-\text{3a}^\text{x}+\sqrt[3]{\text{x}^2}+6\sqrt[4]{\text{x}^{-3}}\Big\}$
$\Big\{\log\Big(\frac{1}{\sqrt{\text{x}}}\Big)+5\text{x}^\text{a}-\text{3a}^\text{x}+\sqrt[3]{\text{x}^2}+6\sqrt[4]{\text{x}^{-3}}\Big\}$
$\frac{\text{d}}{\text{dx}}\Big\{\log\Big(\frac{1}{\sqrt{\text{x}}}\Big)+5\text{x}^\text{a}-\text{3a}^\text{x}+\sqrt[3]{\text{x}^2}+6\sqrt[4]{\text{x}^{-3}}\Big\}$
$=\frac{\text{d}}{\text{dx}} \log\Big(\frac{1}{\sqrt{\text{x}}}\Big)+5\frac{\text{d}}{\text{dx}}(\text{x}^\text{a})-3(\text{a}^\text{x})+\frac{\text{d}}{\text{dx}}(\sqrt[3]{\text{x}^2})+6\frac{\text{d}}{\text{dx}}(\sqrt[4]{\text{x}^{-3}})$
$=\frac{-1}{2}\frac{1}{\text{x}}+5\text{ax}^{\text{a}-1}-3\text{a}^\text{x}\log\text{a}+\frac{2\text{x}^{\frac{-1}{3}}}{3}+\text{6x}^{\frac{-7}{4}}\Big(\frac{-3}{4}\Big)$
$=\frac{-1}{2\text{x}}+5\text{ax}^{\text{a}-1}-3\text{a}^\text{x}\log\text{a}+\frac{2\text{x}^{\frac{-1}{3}}}{3}-\frac{9}{2}\text{x}^{\frac{-7}{4}}$
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| Subject | Mathematics | Physics | Chemistry |
| Mean | 42 | 32 | 40.9 |
| Standard | 12 | 15 | 20 |
| Deviation | | |
| Marks | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 |
| No. of students | 8 | 10 | 15 | 25 | 20 | 18 | 9 | 5 |