On paper it says that the answer to differentiating tan2x is 2(sec(x))^2
Can someone explain to me how to get this answer? My answer is (sec(2x))^2 and I've got no clue where they get the 2 from..
Such type of differentiation is explained in C3.
The general way of differentiating such an expression, tan(y), is to differentiate the part in bracket and multiply it with sec(y)^2.
Your expression is tan(2x).
Differentiating 2x gives you 2. So your differentiated expression should be 2*sec(2x)^2.
To differentiate the tan, you get sec^2. That's that sorted. You then must multiply this by the derivative of the 2x, which is 2. You keep the 2x after the trig function, no matter how many times it is differentiated. So, you have 2sec^2(2x).