What is the derivative of #-x#?

1 Answer
Shwetank Mauria
May 12, 2016

#(df)/(dx)=-1#

Explanation:

Derivative of function #f(x)# is defined as

#(df)/(dx)=Lt_(Deltax->0)(f(x+Deltax)-f(x))/(Deltax)#

As #f(x)=-x#, #f(x+Deltax)=-(x+Deltax)#

Hence #(df)/(dx)=Lt_(Deltax->0)(-(x+Deltax)-(-x))/(Deltax)# or

= #Lt_(Deltax->0)(-x-Deltax+x)/(Deltax)#

= #Lt_(Deltax->0)(-Deltax)/(Deltax)=-1#

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