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to find derivate of cosx/x using first principle method

to find derivate of cosx/x using first principle method

Grade:11

1 Answers

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18 Points
7 years ago
Cox/x so F(x) Lim h>0 = cos(x+h)/(x+h)- (cosx/x)/ h(Taking simple LCM we get)xcos(x+h) - (x+h)cosx/xh(x+h)Open cos(x+h) by cos(a+b)x[cosx.cosh - sinx.sinh]— x.cosx—hcosx/xh(x+h)xcosx(cosh—1)/xh(x+h) —xcosxsinh/xh(x+h)—hcosx/xh(x+h)Since 1—cosh= 2sin^2h/2Therefore —cosx.2sin^2h/2 * h^2/4/ xh(x+h) h^2/2—xsinx/xh(x+h)—cosx/xh(x+h)With limit h>00—xsinx/x^2—cosx/x^2Ans. —xsinx—cosx/x^2

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