We have the function g(x) = sin 9x.
We have to find the second derivative of g(x). We use the chain rule here.
g(x) = sin 9x
=> g'(x) = 9 cos 9x
=> g''(x) = -81 sin 9x
The required second derivative is -81 sin 9x
We'll differentiate the given functin with respect to x, using the chain rule.
g'(x) = [sin (9x)]'
g'(x) = [cos (9x)]*(9x)'
g'(x) = 9*cos (9x)
Now, we'll differentiate the expression of g'(x), with respect to x:
g"(x) = [9*cos (9x)]'
g"(x) = 9*(-sin (9x))*(9x)'
g"(x) = -81sin (9x)
The value of the second derivative of the given function is g"(x) = -81sin (9x).