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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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