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Derivatives — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsDerivatives4 Marks
Question
Differentiate the following function with respect to $(\text{x})$:$\Big\{\log\Big(\frac{1}{\sqrt{\text{x}}}\Big)+5\text{x}^\text{a}-\text{3a}^\text{x}+\sqrt[3]{\text{x}^2}+6\sqrt[4]{\text{x}^{-3}}\Big\}$
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Answer

We have,$\frac{\text{d}}{\text{dx}}\Big\{\log\Big(\frac{1}{\sqrt{\text{x}}}\Big)+5\text{x}^\text{a}-\text{3a}^\text{x}+\sqrt[3]{\text{x}^2}+6\sqrt[4]{\text{x}^{-3}}\Big\}$
$=\frac{\text{d}}{\text{dx}} \log\Big(\frac{1}{\sqrt{\text{x}}}\Big)+5\frac{\text{d}}{\text{dx}}(\text{x}^\text{a})-3(\text{a}^\text{x})+\frac{\text{d}}{\text{dx}}(\sqrt[3]{\text{x}^2})+6\frac{\text{d}}{\text{dx}}(\sqrt[4]{\text{x}^{-3}})$
$=\frac{-1}{2}\frac{1}{\text{x}}+5\text{ax}^{\text{a}-1}-3\text{a}^\text{x}\log\text{a}+\frac{2\text{x}^{\frac{-1}{3}}}{3}+\text{6x}^{\frac{-7}{4}}\Big(\frac{-3}{4}\Big)$
$=\frac{-1}{2\text{x}}+5\text{ax}^{\text{a}-1}-3\text{a}^\text{x}\log\text{a}+\frac{2\text{x}^{\frac{-1}{3}}}{3}-\frac{9}{2}\text{x}^{\frac{-7}{4}}$

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