Question

Find the derivatives of the following function at the indicated points:

(i) 2 cos x at x = π/2

(ii) sin 2x at x = π/2

Answer 1

(i) 2 cos x at x = π/2

Given:

f (x) = 2 cos x

By using the derivative formula,

(ii) sin 2x at x = π/2

Given:

f (x) = sin 2x

By using the derivative formula,

[Since it is of indeterminate form. We shall apply sandwich theorem to evaluate the limit.]

Now, multiply numerator and denominator by 2, we get