If `x = sin theta, y = sin^(3) theta` then `(d^(2)y)/(dx^(2))` at `theta = (pi)/(2)` is …….

Options

A. 3
B. 6
C. `(1)/(6)`
D. `(1)/(3)`

Answer

B

Explanation

We have, `x = sin theta, y = "sin"^(3) theta`
`:. (dy)/(dx) = ((dy)/(d theta))/((dx)/(d theta)) = (3"sin"^(2) theta(cos theta))/(cos theta)`
`implies (dy)/(dx) = 3 "sin"^(2) theta`
Now, `(d^(2)y)/(dx^(2)) = 3 (2 "sin" theta cos theta) (d theta)/(dx)`
at `theta = (pi)/(2), (d^(2) y)/(dx^(2)) = 6 "sin" ((pi)/(2)) = 6 xx 1 = 6`