Question

derive
3cos (x/2)

Answer 1

To derive 3cos(x/2), we will use the chain rule. The chain rule states that if we have a function f(g(x)), then its derivative is f'(g(x)) * g'(x).

Let's apply the chain rule step by step:

Let f(x) = 3cos(x) and g(x) = x/2.

To find the derivative of 3cos(x/2), we need to find the derivative of 3cos(x) and the derivative of x/2 and then multiply them together.

Derivative of 3cos(x):
Using the chain rule, we have f'(x) = -3sin(x).

Derivative of x/2:
The derivative of x/2 is simply 1/2.

Now, applying the chain rule, we multiply the derivatives together:

f'(g(x)) * g'(x) = -3sin(x/2) * (1/2).

Therefore, the derivative of 3cos(x/2) is (-3/2)sin(x/2).