Question

Find the derivative of from the first principle.​

Answer 1

Step-by-step explanation:

Let f(x)=x21 

Thus according to first principle,

f′(x)=h→0limhf(x+h)−f(x)

=h→0limh(x+h)1−x21

=h→0limh1[x2(x+h)2x−(x+h)2]

=h→0limh1[x2(x+h)2x2−x2−h2−2hx]

=h→0limh1[

[x2(x+h)2−h2−2hx]

=h→0lim[x2(x+h)2−h−2x]

=x2(x+0)20−2x=x3−2