How do you use the limit definition to find the derivative of #y=-4x-5#?

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How do you use the limit definition to find the derivative of #y=-4x-5#?

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Answer 1 · 2016-10-31T23:06:44

# dy/dx = -4#

Explanation:

By definition # f'(x) =lim_(hrarr0)( (f(x+h)-f(x))/h ) #

So, with # y=-4x-5 # we have:
# dy/dx = lim_(hrarr0)( ( (-4(x+h)-5) - (-4x-5) ) / h )#
# :. dy/dx = lim_(hrarr0)( ( (-4x-4h-5) - (-4x-5) ) / h )#
# :. dy/dx = lim_(hrarr0)( ( -4x-4h-5 +4x+5 ) / h )#
# :. dy/dx = lim_(hrarr0)( -(4h) / h )#
# :. dy/dx = lim_(hrarr0)( -4 )#
# :. dy/dx = -4#

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How do you use the limit definition to find the derivative of #y=-4x-5#?

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