If f(x)=sin(2x), find f"(x)

A. 2cos(2x)
B. -4sin(2x)
C. -2sin(2x)
D. -4sinx
E. None of these

Is it B from using chain rules?

Yes, you are correct. To find the second derivative of f(x) = sin(2x), you can use the chain rule.

The chain rule states that if you have a composite function, such as f(g(x)), then the derivative of that function with respect to x is given by the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function with respect to x.

In this case, the outer function is sin(u), and the inner function is 2x.

To find f'(x), the derivative of f(x), we can apply the chain rule:

f'(x) = 2cos(2x)

To find f''(x), the second derivative of f(x), we can apply the chain rule again:

f''(x) = (d/dx)(f'(x))
= (d/dx)(2cos(2x))
= -4sin(2x)

Therefore, the second derivative of f(x) = sin(2x) is -4sin(2x), which corresponds to option B.