Question

differentiation cos ² x​

Answer 1

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Let, y=cos2x.

Let, y=cos2x.Then, y can be written as y=(cosx)2.

Let, y=cos2x.Then, y can be written as y=(cosx)2.Now dydx=d(cosx)2dx

Let, y=cos2x.Then, y can be written as y=(cosx)2.Now dydx=d(cosx)2dx=> dydx=d(cosx)2d(cosx)∙d(cosx)dx [By chain rule]

dydx=d(cosx)2d(cosx)∙d(cosx)dx [By chain rule]=> dydx=2(cosx)1∙(−sinx)

dydx=2(cosx)1∙(−sinx)=> dydx=−2(sinx)(cosx)=−sin2x

dydx=−2(sinx)(cosx)=−sin2xTherefore the differentiation of cos2x is −sin2x.

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