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How do you find the derivative of #f(x)=-5x# using the limit process?

1 Answer

Nov 3, 2017

see below

Explanation:

the definition

#(dy)/(dx)=Lim_(hrarr0)((f(x+h)-f(x))/h)#

#f(x)=-5x#

#(dy)/(dx)=Lim_(hrarr0)((-5(x+h)- (-5x))/h)#

#(dy)/(dx)=Lim_(hrarr0)((cancel(-5x)-5hcancel(+5x))/h)#

#(dy)/(dx)=Lim_(hrarr0)((-5cancel(h))/cancel(h))#

#(dy)/(dx)=Lim_(hrarr0)(-5)=-5#

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