What is the derivative of y=tan⁡(x)?

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Raymond Foley · Accepted Answer

The derivative of tan⁡x  is  sec2xTo see why, you&#039;ll need to know a few results. First, you need to know that the derivative of sin⁡x  is  cos⁡x.Once all those pieces are in place, the differentiation goes as follows:ddxtan⁡x=ddxsin⁡xcos⁡x=cos⁡x⋅cos⁡x−sin⁡x⋅(−sin⁡x)cos2x  (using Quotient Rule)=cos2x+sin2xcos2x=1cos2x  (using the Pythagorean Identity)=sec2x

Chanell Sanborn · Accepted Answer

Given, y=tan⁡x.  Let u=sin⁡x  and  v=cos⁡x  On applying quotient rule on y=sin⁡xcos⁡x, we get,  ∵dydx=v.dudx−u.dvdxv2  ⇒dydx=cos⁡x⋅cos⁡x−sin⁡x−sin⁡xcos2x  ⇒dydx=cos2x+sin2xcos2x  ⇒dydx=1cosx  ⇒dydx=sec2(x)  Thus, the derivative of y=tan⁡(x)  is  sec2(x)

RizerMix · Accepted Answer

y=tan⁡(x)Differentiate both sides of the equation.ddx(y)=ddx(tan⁡(x))The derivative of y with respect to x is y&#039;.y&#039;The derivative of tan⁡(x) with respect to x is sec2⁡(x)sec2⁡(x)Reform the equation by setting the left side equal to the right side.y′=sec2⁡(x)Replace y&#039; with dydxdydx=sec2⁡(x)

What is the derivative of y=\tan(x)?

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