How can I evaluate g''(f)

Question

Q. If g(θ)= sin(θ)/θ, find g'(f), g''(f).

I got g'(f) for (θcos(θ)-sin(θ))/θ^2

But when I tried to evaluate g''(f), I got the wrong answer.

I want to know the process of the evaluation and answer as soon as possible.

Answer 1

You got g '(θ) correct.

If you rewrite g '(θ) = -cos(θ)/θ - sin(θ)/θ² it is easier to find g ''(θ)

g"(θ) = (-sin(θ)θ-cos(θ))/θ² - (cos(θ)θ² - 2sin(θ)θ)/θ⁴

with some algebra manipulation:

g"(θ) = -((θ²-2)sin(θ)+2θcos(θ))/θ³