How do you use the definition of a derivative to find the derivative of $f(x)=2x$ ?

Question

1594 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-22T09:18:10

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

defn. $""(dy)/(dx)=Lim_(hrarr0)((f(x+h)-f(x))/h)$

for $""y=2x$

$""(dy)/(dx)=Lim_(hrarr0)((2(x+h)-2x)/h)$

$""(dy)/(dx)=Lim_(hrarr0)((cancel(2x)+2hcancel(-2x))/h)$

$""(dy)/(dx)=Lim_(hrarr0)((2cancel(h))/cancel(h))$

$(dy)/(dx)=2$

How do you use the definition of a derivative to find the derivative of f(x)=2xf(x)=2x?