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Differentiate \sin (\cot \sqrt{x}) with respect to x.

Option: 1

-\frac{\cot \sqrt{x} \csc ^2 \sqrt{x}}{\sqrt{x}}


Option: 2

-\frac{\csc \cot (\sec \sqrt{x}) \cdot \sec \sqrt{x} \tan \sqrt{x}}{2 \sqrt{x}}


Option: 3

-\frac{\sec \tan (\cot \sqrt{x})) \cdot \csc ^2 \sqrt{x}}{2 \sqrt{x}}


Option: 4

-\frac{\cos (\cot \sqrt{x}) \cdot \csc ^2 \sqrt{x}}{2 \sqrt{x}}


Answers (1)

The given term is: 

\sin (\cot \sqrt{x})
Let y= \sin (\cot \sqrt{x})

Then differentiating w.r.t.x,

\frac{d y}{d x}=\cos (\cot \sqrt{x}) \cdot \frac{d}{d x}(\cot \sqrt{x})
=\cos (\cot \sqrt{x}) \cdot\left(-\csc ^2 \sqrt{x}\right) \cdot \frac{d}{d x}(\sqrt{x})
=-\cos (\cot \sqrt{x}) \cdot \csc ^2 \sqrt{x} \cdot \frac{1}{2 \sqrt{x}}
=-\frac{\cos (\cot \sqrt{x}) \cdot \csc ^2 \sqrt{x}}{2 \sqrt{x}}


 

Posted by

Sumit Saini

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