The derivative of the function f(x) = tan(2x) at x = pi/6 can be calculated using the chain rule. The derivative f'(x) is found to be 2 * sec^2(2x). Evaluating this at x = pi/6 gives f'(pi/6) = 2 * sec^2(pi/3). Since sec(pi/3) can be expressed in terms of cosine, the final answer simplifies to 2 * (2) = 4, as sec(pi/3) = 2.
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The derivative of tan(pi/3) is zero. tan(pi/3) is a constant, and the derivative of any constant is zero.SAT2400 said:Homework Statement
If f(x)= tan(2x), then f'(pi/6) =
Homework Equations
deriv. of tan(pi/3)
Yes. There are a few angles whose trig functions you should have memorized - 0, pi/6, pi/4, pi/3, pi/2, as well as their supplements and combinations with pi/2, pi, and so on. You should also have memorized all of the six trig functions in terms of the sine or cosine.SAT2400 said:The Attempt at a Solution
How can I solve this? I am not supposed to use a calculator?? tan(pi/3) ...am I supposed to memorize this?
jav said:And now how can you simplify that using the definition of sec?