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NCERT Class XI Mathematics - Limits and Derivatives - Solutions

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Question : 70 of 72
Marks: +1, -0
x2cos⁡(π/4)sin⁡x\frac{x^2 \cos(\pi/4)}{\sin x}
Solution:  
Let f (x) = x2cos⁡(π/4)sin⁡x\frac{x^2 \cos(\pi/4)}{\sin x} ... (i)
Differentiating (i) with respect to x, we get
ddx\frac{d}{dx} [f (x)] = cos⁡(π/4)[sin⁡x⋅(x2)′−(x2)(sin⁡x)′sin⁡2x]\cos(\pi/4)\left[\frac{\sin x \cdot (x^2)' - (x^2)(\sin x)'}{\sin^2 x}\right]
= cos⁡(π/4)[sin⁡x⋅2x−x2cos⁡xsin⁡2x]\cos(\pi/4)\left[\frac{\sin x \cdot 2x - x^2 \cos x}{\sin^2 x}\right]
= xcos⁡(π/4)[2sin⁡x−xcos⁡xsin⁡2x]x \cos(\pi/4)\left[\frac{2\sin x - x \cos x}{\sin^2 x}\right]
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