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How do you use the limit definition to find the derivative of $y=-3x-3$ ?

1 Answer

Oct 15, 2016

$dy/dx=-3$

Explanation:

By definition:
$dy/dx=lim_(h->0)(f(x+h)-f(x))/h$

so, with $y=-3x-3$ we have:

$dy/dx=lim_(h->0)((((-3)(x+h)-3)-(-3x-3))/h)$
$:. dy/dx=lim_(h->0)((-3x -3h-3+3x+3)/h)$
$:. dy/dx=lim_(h->0)(-3h)/h$
$:. dy/dx=-3$

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