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y-x-Find-dy-dx-by-first-principle-




Question Number 162675 by Mathematification last updated on 31/Dec/21
y = (√x)  Find   (dy/dx)  by first principle.
y=xFinddydxbyfirstprinciple.
Answered by tounghoungko last updated on 31/Dec/21
 (dy/dx) = lim_(h→0)  ((f(x+h)−f(x))/h)         = lim_(h→0)  (((√(x+h))−(√x))/h) = lim_(h→0)  (h/(h ((√(x+h))+(√x))))        = lim_(h→0)  (1/( (√(x+h))+(√x))) = (1/(2(√x)))
dydx=limh0f(x+h)f(x)h=limh0x+hxh=limh0hh(x+h+x)=limh01x+h+x=12x

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