Question

find the derivative of 1/tan(2x)

Answer 1

look in your book for the derivative of cotangent

Answer 2

followed by chain rule :)

Answer 3

cotangent is -csc^2. so far it would be \[\frac{ 2\csc ^{2}x }{ (\tan2x)^{2} }\]

Answer 4

After that i get kind of confused on how to solve the rest.

Answer 5

hold the phone
what is the derivative of cotangent?

Answer 6

-csc^2u

Answer 7

actually all you have to remember is the derivative of tangent

Answer 8

since the derivative of tangent is secant squared, you get the derivative of cotangent is minus cosecant squared

Answer 9

in this case you have \(\cot(2x)\) and its derivative is therefore
\[-2\csc^2(2x)\]

Answer 10

but when you use the chain rule it would turn positive because of the subtraction sign. u'v-uv'