Question

प्रथम सिद्धांत से निम्नलिखित फलनों के अवकलज ज्ञात कीजिए : $(- x)^{-1}$

Answer 1

f'(x) =  x⁻²  यदि  f(x) =  (- x)⁻¹

Step-by-step explanation:

प्रथम सिद्धांत

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

f(x) =  (- x)⁻¹

=> f(x) = -1/x

f'(x) =  Lim  h → 0     ( -1/(x + h) - (-1/x) )/h

=> f'(x) = Lim  h → 0  ( 1/x - 1/(x + h) )/h

=> f'(x) = Lim  h → 0  (x + h - x )/hx(x + h)

=> f'(x) = Lim  h → 0  h/hx(x + h)

=> f'(x) = Lim  h → 0  1/x(x + h)

=> f'(x)   = 1/x(x + 0)

= 1/x²

= x⁻²

f'(x) =  x⁻²

और पढ़ें

फलनों के अवकलन ज्ञात कीजिए

brainly.in/question/15778266

सीमाओं के मान प्राप्त कीजिए :  [tex]\lim_{x\rightarrow3}\dfrac{x^4 - 81

brainly.in/question/15778085

सीमाओं के मान प्राप्त कीजिए

brainly.in/question/15778083

Answer 2

$\huge\star\mathfrak\blue{{Answer:-}}$

प्रथम सिद्धांत

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

f(x) = Cos(x - π/8)

f'(x) = Lim h → 0 (Cos(x + h - π/8) - Cos(x - π/8) )/h

=> f'(x) = Lim h → 0 (Cos(x -π/8 + h) - Cos(x - π/8 ) )/h

CosA + B) =CosACosB -SinASinB

A = x -π/8 B = h

=> f'(x) = Lim h → 0 Cos(x -π/8)Cosh - Sin(x -π/8)Sinh - Cos(x - π/8 )/h

=> f'(x) = Lim h → 0 Cos(x -π/8)Cosh - Cos(x - π/8 )/h - Sin(x -π/8)Sinh/h

Lim h → 0 Sinh/h = 1

=> f'(x) = Lim h → 0 Cos(x -π/8)(Cosh - 1) - Sin(x -π/8)

=> f'(x) = Cos(x -π/8)(Cos0 - 1) - Sin(x -π/8)

=> f'(x) = Cos(x -π/8)(1 - 1) - Sin(x -π/8)

=> f'(x) = Cos(x -π/8)(0) - Sin(x -π/8)

=> f'(x) = 0 - Sin(x -π/8)

=> f'(x) = - Sin(x -π/8)

f'(x) = - Sin(x -π/8) यदि f(x) = Cos(x - π/8)