Question

प्रथम सिद्धांत से निम्नलिखित फलन का अवकलज ज्ञात कीजिए:

`1/x^2`

Answer 1

`f(x) = 1/x^2, f(x + h) = 1/(x + h)^2`

∴ `f(x + h) - f(x) = 1/(x + h)^2 - 1/x^2`

= `(x^2 - (x + h)^2)/(x^2 (x + h)^2)`

= `(x^2 - [x^2 + 2xh + h^2])/(x^2 (x + h)^2)`

= `(-h(2x + h))/(x^2(x + h)^2)`

`f'(x) = lim_(h → 0) (f(x + h) - f(x))/h`

= ` lim_(h → 0) (-h(2x + h))/(x^2 (x + h)^2 h)`

= `(-2x)/(x^2x^2)`

= `-2/x^3`