# How do you use the limit definition of the derivative to find the derivative of #y=-2x+5#?

##### 1 Answer

Jan 1, 2017

#### Explanation:

The definition of the derivative of

# f'(x)=lim_(h rarr 0) ( f(x+h)-f(x) ) / h #

So Let

# f(x+h) = -2(x+h) + 4 #

# " "= -2x-2h + 4 #

And so

# f(x+h)-f(x) = (-2x-2h + 4 ) - (-2x+4) #

# " "= -2x-2h + 4 +2x-4 #

# " "= -2h #

And so the derivative of

# \ \ \ \ \ dy/dx = lim_(h rarr 0) (-2h) / h #

# " " = lim_(h rarr 0) -2 #

# " " = -2 #

# :. dy/dx = -2 #