Final answer:
The second derivative of the function 5sin(x)cos(x) is -10sin(2x).
Step-by-step explanation:
The second derivative of the function 5sin(x)cos(x) can be found by taking the derivative of the first derivative. Let's start by finding the first derivative:
First derivative: (5sin(x)cos(x))' = 5(cos(x)cos(x) - sin(x)sin(x)) = 5(cos^2(x) - sin^2(x)) = 5cos(2x)
Now, let's find the second derivative:
Second derivative: (5cos(2x))' = -10sin(2x)
So, the correct answer is a) -5sin(2x).