How do you find f'(x) using the definition of a derivative for #f(x)=5.5x^2 - x + 4.2 #?

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Answer 1 · 2015-09-26T20:53:43

See the explanation.

#f'(x)=lim_(Deltax->0)(f(x+Deltax)-f(x))/(Deltax)#

#lim_(Deltax->0) (5.5(x+Deltax)^2-(x+Deltax)+4.2-(5.5x^2-x+4.2))/(Deltax)#

#lim_(Deltax->0) (5.5x^2+11xDeltax+5.5Delta^2x-x-Deltax+4.2-5.5x^2+x-4.2) /(Deltax)#

#lim_(Deltax->0) (11xDeltax+5.5Delta^2x-Deltax) /(Deltax)=lim_(Deltax->0) (11x+5.5Deltax-1)#

#f'(x)=11x-1#