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Derivatives — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSDerivatives3 Marks
Question
Differentiate the following function with respect to $(\text{x})$:$(\text{a}_0\text{x}^\text{n}+\text{a}_1\text{x}^{\text{n}-1}+\text{a}_2\text{x}^{\text{n}-2}+\dots+\text{a}_{\text{n}-1}+\text{a}_\text{n})$
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Answer

We have,$\frac{\text{d}}{\text{dx}}(\text{a}_0\text{x}^\text{n}+\text{a}_1\text{x}^{\text{n}-1}+\text{a}_2\text{x}^{\text{n}-2}+\dots+\text{a}_{\text{n}-1}+\text{a}_\text{n})$
$=\text{a}_0\frac{\text{d}}{\text{dx}}(\text{x})^\text{n}+\text{a}_1\frac{\text{d}}{\text{dx}}(\text{x})^{\text{n}-1}+\text{a}_2\frac{\text{d}}{\text{dx}}(\text{x})^{\text{n}-2}+\dots+\text{a}_{\text{n}-1}\frac{\text{d}}{\text{dx}}+\text{a}_\text{n}\frac{\text{d}}{\text{dx}}(1)$
$=\text{na}_0\text{x}^{\text{n}-1}+(\text{n}-1)\text{a}_1\text{x}^{\text{n}-2}+\dots+\text{a}_{\text{n}-1}+0$
$=\text{na}_0\text{x}^{\text{n}-1}+(\text{n}-1)\text{a}_1\text{x}^{\text{n}-2}+\dots+\text{a}_{\text{n}-1}$

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