Derivative of tan(2x) at pi/6 without a calculator

[SAT2400]

Homework Statement

If f(x)= tan(2x), then f'(pi/6) =

Homework Equations

deriv. of tan(pi/3)

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?

 

[Pinu7]

What is f'(x) ?
Hint: use the chain rule.

 

[SAT2400]

tan(pi/3) ' = sec^2(pi/3) is it??

 

[jav]

And now how can you simplify that using the definition of sec?

 

[Mark44]

Homework Statement

If f(x)= tan(2x), then f'(pi/6) =

Homework Equations

deriv. of tan(pi/3)

The derivative of tan(pi/3) is zero. tan(pi/3) is a constant, and the derivative of any constant is zero.

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?

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.

 

[Pinu7]

And now how can you simplify that using the definition of sec?

Can you write sec x in terms of sine and/or cosine? You should have memorized the values of sin(pi/3) and cos(pi/3)