How do you find f'(x) using the definition of a derivative for #f(x)=sqrt(2x)#?

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Answer 1 · 2015-10-06T16:48:42

#f'(x)=1/(sqrt(2x))#

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

#f'(x)=lim_(h->0) (sqrt(2(x+h))-sqrt(2x))/h*(sqrt(2(x+h))+sqrt(2x))/(sqrt(2(x+h))+sqrt(2x))#

#f'(x)=lim_(h->0) (2(x+h)-2x)/(h(sqrt(2(x+h))+sqrt(2x)))#

#f'(x)=lim_(h->0) (2x+2h-2x)/(h(sqrt(2(x+h))+sqrt(2x)))#

#f'(x)=lim_(h->0) (2h)/(h(sqrt(2(x+h))+sqrt(2x)))#

#f'(x)=lim_(h->0) 2/(sqrt(2(x+h))+sqrt(2x))#

#f'(x)=lim_(h->0) 2/(sqrt(2(x+0))+sqrt(2x))#

#f'(x)=2/(sqrt(2x)+sqrt(2x))#

#f'(x)=2/(2sqrt(2x))#

#f'(x)=1/(sqrt(2x))#