Question

Find the Second Derivative 5sin(x)cos(x):

a) -5sin(2x)
b) 5cos(2x)
c) -5cos(2x)
d) 5sin(2x)

Answer 1

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).