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

1 Answer
Steve M
Oct 31, 2016

dy/dx = -4dydx=−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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