Use the quotient rule and the derivatives of the sine and cosine functions to prove that ddx(cot⁡x)=−csc2x.

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Leonard Stokes · Accepted Answer

Step 1: We haveprove that&amp;nbsp;d&amp;nbsp;dx&amp;nbsp;(cot⁡x)=−csc2x&amp;nbsp;Step 2: Solution&amp;nbsp;Consider the meaning of cotangentd&amp;nbsp;dx&amp;nbsp;(cos⁡xsin⁡x)&amp;nbsp;sin⁡xd&amp;nbsp;dx&amp;nbsp;(cos⁡x)−cos⁡xd&amp;nbsp;dx&amp;nbsp;(sin⁡x)sin2x&amp;nbsp;sin⁡x⋅−sin⁡x−cos⁡x⋅cos⁡xsin2x&amp;nbsp;−sin2x−cos2xsin2x&amp;nbsp;Use the Pythagorean identity&amp;nbsp;−1sin2x&amp;nbsp;Use the definition of cosecant&amp;nbsp;−csc2x&amp;nbsp;Step 3: Conclusion&amp;nbsp;Using the quotient rule and derivatives of sine and cosine we proved that&amp;nbsp;d&amp;nbsp;dx&amp;nbsp;(cot⁡x)=−csc2x

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

Use the quotient rule and the derivatives of the sine and cosine functions to pr

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