Question

If f(x) = cos x - 6 tan x, then

a) f'(x) = -sin x - 6/cos² x
b) f'(x) = sin x - 6/cos² x
c) f'(x) = -sin x - 6 sec² x
d) f'(x) = sin x + 6 sec² x

Answer 1

The derivative of f(x) = cos x - 6 tan x, through the use of differentiation rules, is found to be f'(x) = -sin x - 6 sec² x, which corresponds to option (c).

Step-by-step explanation:

The question requires us to find the derivative of the function f(x) = cos x - 6 tan x. To find the derivative, f'(x), we apply the differentiation rules to each term separately.

The derivative of cos x is -sin x. The derivative of tan x is sec² x. Recall that sec x = 1/cos x, so sec² x = 1/cos² x. Therefore, the derivative of -6 tan x is -6 times the derivative of tan x, which gives us -6 sec² x.

Combining these, we get f'(x) = -sin x - 6 sec² x. Hence, the correct option is (c) f'(x) = -sin x - 6 sec² x. It is important to choose only one option that correctly reflects the derivative, and in this case, option c is the mention correct option in final answer.