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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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