Final answer:
The derivative of f(x) = 6√x + 5cosx is f'(x) = 3/√x - 5sinx.
Step-by-step explanation:
To find the derivative of f(x) = 6√x + 5cosx, we can use the rules of differentiation. Let's take it step by step:
- For the first term, the derivative of 6√x with respect to x is 3/√x.
- For the second term, the derivative of 5cosx with respect to x is -5sinx.
Therefore, the derivative of f(x) = 6√x + 5cosx is f'(x) = 3/√x - 5sinx.