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Limits and Derivatives — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSLimits and Derivatives3 Marks
Question
Differentiate the following functions.
$(\sin\text{x}+\cos\text{x})^{2}$
✓

Answer

$\frac{\text{d}}{\text{dx}}(\sin\text{x}+\cos\text{x})^{2}$ 
$=\frac{\text{d}}{\text{dx}}(\sin\text{x}+\cos\text{x})(\sin\text{x}+\cos\text{x})$
$=(\sin\text{x}+\cos\text{x})\frac{\text{d}}{\text{dx}}(\sin\text{x}+\cos\text{x})$
$=(\sin\text{x}+\cos\text{x})\frac{\text{d}}{\text{dx}}(\sin\text{x}+\cos\text{x})\\+(\sin\text{x}+\cos\text{x})\frac{\text{d}}{\text{dx}}(\sin\text{x}+\cos\text{x})$
$=2(\sin\text{x}+\cos\text{x})\frac{\text{d}}{\text{dx}}(\sin\text{x}+\cos\text{x})$
$=2(\sin\text{x}+\cos\text{x})(\cos\text{x}-\sin\text{x})$
$=2(\cos^{2}\text{x}-\sin^{2}\text{x})$
$=2\cos2\text{x}$ 
Hence, the required answer is $2\cos2\text{x}.$

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