find the derivative of (-x) using first principles

ncert cbse 11th chapter 13 limits and derivatives

1

(i)  find the derivative of (-x) using first principles

let f(x) = (-x)

let h be a small increment in x

f(x+h) = -(x+h)

f(x+h) - f(x) = [ -(x+h)] - [-x] = -x-h+x = (-h)

{f(x+h) - f(x)} / {h} = (-h) / {h} = (-1)

taking limit as h --> 0

f ' (x) = (-1)

(ii)   find the derivative of [ (-x)^(-1) ] using first principles

let f(x) = [ (-x)^(-1) ]

f(x) = (-1) / [x]

f(x+h) = (-1) / [x+h]

f(x+h) - f(x) = [(-1) / [x+h] ] - [ (-1) / [x] ]

={(-x+x+h) / x(x+h)}

=h / x(x+h)

{f(x+h) - f(x)} / {h} = 1 / [ x(x+h) ]

taking limit as h --> 0

f ' (x) = 1 / [x(x+0)]

=1/[(x^2)]

13. limits and derivatives
miscellaneous exercise

1.

(i)  find the derivative of (-x) using first principles
solution

(ii)   find the derivative of [ (-x)^(-1) ] using first principles

solution




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