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prove-using-the-first-principle-that-the-derivative-of-sin-x-is-cox-x-and-that-the-derivative-of-cos-x-is-sinx-




Question Number 129033 by oustmuchiya@gmail.com last updated on 12/Jan/21
prove using the first principle that  the derivative of sin x is cox x and  that the derivative of cos x is  −sinx
proveusingthefirstprinciplethatthederivativeofsinxiscoxxandthatthederivativeofcosxissinx
Commented by bramlexs22 last updated on 12/Jan/21
y=sin x  y′ = lim_(h→0) ((sin (x+h)−sin x)/h)       = lim_(h→0)  ((2cos (((2x+h)/2))sin ((h/2)))/h)      = lim_(h→0) ((sin (h/2))/h) × 2cos x   = cos x
y=sinxy=limh0sin(x+h)sinxh=limh02cos(2x+h2)sin(h2)h=limh0sin(h/2)h×2cosx=cosx

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