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Derivatives — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSDerivatives2 Marks
Question
Differentiate the following functions with respect to x:$\frac{\text{x}^2+1}{\text{x}+1}$
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Answer

$\frac{\text{d}}{\text{dx}}\Big(\frac{\text{x}^2+1}{\text{x}+1}\Big)=\frac{(\text{x}+1)\frac{\text{d}}{\text{dx}}(\text{x}^2+1)\frac{\text{d}}{\text{dx}}(\text{x}+1)}{(\text{x}+1)^2}$$=\frac{(\text{x}+1)\times\text{2x}-(\text{x}^2+1)\times1}{(\text{x}+1)^2}$
$=\frac{\text{2x}^2+\text{2x}-\text{x}^2-1}{(\text{x}+1)^2}$
$=\frac{\text{x}^2+\text{2x}-1}{(\text{x}+1)^2}$

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