# Prove that the derivative of tan(2x) - cot(2x) equals...

Let f(x) = tan(2x) - cot(2x) defined on x∈]0,π/4[

Prove that derivative of f(x) is 16/1-cos(8x)

What I did was:

2 * Sin^2(2x) + 2 * Cos^2(2x) / Cos^2(2x) + Sin^2(2x)

If I factor the 2, I reach:

2 * (Sin^2(2x) + Cos^2(2x) / 1+cos(4x)/2 + 1-cos(4x)/2

2 * 1/ 1 = 2?

What went wrong?

Mark44
Mentor
Let f(x) = tan(2x) - cot(2x) defined on x∈]0,π/4[

Prove that derivative of f(x) is 16/1-cos(8x)
Did you really mean to write ##\frac{16}{1} - cos(8x)##? If not, use parentheses around the terms in the denominator.
NooDota said:
What I did was:

2 * Sin^2(2x) + 2 * Cos^2(2x) / Cos^2(2x) + Sin^2(2x)
Show how you got this. Also, when the numerator or denominator of a fraction has two or more terms, you must put parentheses around them.
NooDota said:
If I factor the 2, I reach:

2 * (Sin^2(2x) + Cos^2(2x) / 1+cos(4x)/2 + 1-cos(4x)/2

2 * 1/ 1 = 2?

What went wrong?

Okay, nvm, solved it.

In the denominator, I turned the multiplication to addition, which is why I got a wrong result.