Question

Differentiate each of the following from first principles:
(i) 2/x
(ii) 1/√x

(iii) 1/x³

Answer 1

(i) 2/x

Given:

f (x) = 2/x

By using the formula,

∴ Derivative of f(x) = 2/x is -2x^-2

(ii) 1/√x

Given:

f (x) = 1/√x

By using the formula,

When h = 0, we get

∴ Derivative of f(x) = 1/√x is -1/2 x^-3/2

(iii) 1/x³

Given:

f(x) = 1/x³

By using the formula,

When h = 0, we get

∴ Derivative of f(x) = 1/x³ is -3x^-4