How do you find the second derivative of y=Acos(Bx)?

1 Answer
Aug 19, 2017

Well, start with the first derivative.
Treat it like the product of two functions: f(x) * g(x)
where f(x) = A (just a constant) and g(x) = cos(Bx)

so (df(x))/dx = 0.
and (dg(x)/dx) = -Bsin(BX) (used the chain rule here.)

So, by the product rule, the deriv. of the product f(x) * g(x) =

((df(x))/dx) g(x) + f(x)((dg(x))/dx)

in this case, that works out to -ABsin(BX)

Now, just do it again:

d/dx(-ABsin(BX)) = -AB^2cos(BX) (by the chain rule)

GOOD LUCK!