# derivative of cot

(Math | Calculus | Derivatives | Table Of)

sin x = cos x Proofcsc x = -csc x cot x Proof
cos x = - sin x Proofsec x = sec x tan x Proof
tan x = sec2 x Proofcot x = - csc2 x Proof

What is the derivative of cot 2x?
To apply the Chain Rule, set u u as 2x 2 x . The derivative of cot(u) cot ( u ) with respect to u u is −csc2(u) - csc 2 ( u ) .

What is the differentiation of cot Theta?
I have always seen the derivative of tan(x) as sec^2(x) and the derivative of cot(x) as -csc^2(x). This seems to be the standard, and I have never seen it otherwise. However, Sal is using 1/cos^2(x) as the derivative of tan(x) and -1/sin^2(x) as the derivative of cot(x).

What is COTX?
What is 'cotx'? cot is a short way to write 'cotangent'. This is the reciprocal of the trigonometric function 'tangent' or tan(x). Therefore, cot(x) can be simplified to 1/tan(x). Using trigonometric rules, an alternative way to write 1/tan(x) is cos(x)/sin(x).

What is the differentiation of cot Theta?
I have always seen the derivative of tan(x) as sec^2(x) and the derivative of cot(x) as -csc^2(x). This seems to be the standard, and I have never seen it otherwise. However, Sal is using 1/cos^2(x) as the derivative of tan(x) and -1/sin^2(x) as the derivative of cot(x).