Question

Differentiate the following from first principles:

(i) sin √2x

(ii) cos √x

Answer 1

(i) sin √2x

Given:

f (x) = sin √2x

f (x + h) = sin √2(x+h)

By using the formula,

To use the sandwich theorem to evaluate the limit, we need

(ii) cos √x

Given:

f (x) = cos √x

f (x + h) = cos √(x+h)

By using the formula,

To use the sandwich theorem to evaluate the limit, we need