20 Differentiate 2x-12x+1 with respect to x, from first principle - Maths - Limits and Derivatives

Question

20   D i f f e r e n t i a t e   2 x - 1 2 x + 1   w
i t h   r e s p e c t   t o   x ,   f r o m
  f i r s t   p r i n c i p l e

Neha Sethi · Accepted Answer

Dear student
Let fx=2x-12x+1Then fx+h=2x+h-12x+h+1=2x+2h-12x+2h+1So, ddxfx=limh→0fx+h-fxh=limh→02x+2h-12x+2h+1-2x-12x+1h=limh→02x+2h-12x+1-2x-12x+2h+1h2x+12x+2h+1=limh→02x-12x+1+2h2x+1-2x+12x-1-2h2x-1h2x+12x+2h+1=limh→02h2x+1-2h2x-1h2x+12x+2h+1=limh→0h4x+2-4x+2h2x+12x+2h+1=limh→0h2+2h2x+12x+2h+1=limh→04hh2x+12x+2h+1=42x+12x+1=42x+12
Regards

20 . D i f f e r e n t i a t e 2 x - 1 2 x + 1 w i t h r e s p e c t t o x , f r o m f i r s t p r i n c i p l e .

$20 . D i f f e r e n t i a t e \frac{2 x - 1}{2 x + 1} w i t h r e s p e c t t o x, f r o m f i r s t p r i n c i p l e .$