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Derivatives — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsDerivatives3 Marks
Question
Differentiate the following functions with respect to x:$\frac{\sec\text{x}-1}{\sec\text{x}+1}$
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Answer

We have,$\frac{\text{d}}{\text{dx}}\Big(\frac{\sec\text{x}-1}{\sec\text{x}+1}\Big)$
Using quotient rule, we get
$\frac{(\sec\text{x}+1)\frac{\text{d}}{\text{dx}}(\sec\text{x}-1)-(\sec\text{x}-1)\frac{\text{d}}{\text{dx}}(\sec\text{x}+1)}{(\sec\text{x}+1)^2}$
$=\frac{(\sec\text{x}+1)(\sec\text{x}\tan\text{x})-(\sec\text{x}-1)(\sec\text{x}\tan\text{x})}{(\sec\text{x}+1)^2}$
$=\frac{\sec\text{x}\tan\text{x}(\sec\text{x}+1-\sec\text{x}+1)}{(\sec\text{x}+1)^2}$
$=\frac{2\sec\text{x}\tan\text{x}}{(\sec\text{x}+1)^2}$

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