Question

find The derivative of f(x)=1/√x by the first principle ​

Answer 1

Answer:

- 1 / 2x³/²

Step-by-step explanation:

plzz refer the attachment

(1) Let f ( x ) = 1 / √x

f ( x + h ) = 1 / √(x+h)

(2) Now appying formula of first principle

f¹(x) = f(x+h) - f(x) / h

lim h-----> 0

(3) In seventh step we multiply numerator and denominator by the conjugate of numerator and applying formula as follows

a² - b² = (a + b ) ( a - b )

(4) Then putting h = 0 in 13th step

(5) d/ dx (1 / √x ) = - 1 / 2x³/²

Answer 2

Answer:

Step-by-step explanation:

1x /√ x

x ^ −1/2

−1/2 x^−1/2−1

−1/2x^−3/2

−1/2√x^3