2. Derivatives of Csc, Sec and Cot Functions
by M. Bourne
By using the quotient rule and trigonometric identities, we can obtain the following derivatives:
In words, we would say:
The derivative of csc x is -csc x cot x,
The derivative of sec x is sec x tan x and
The derivative of cot x is -csc2x.
If u = f(x) is a function of x, then by using the chain rule, we have:
Example 1:
Find the derivative of s = sec(3t + 2).
You can change the function in this LiveMath document.
Example 2:
Find the derivative of x = θ3 csc 2θ.
Example 3:
Find the derivative of y = sec43x.
Exercises
1. Find the derivative of y = csc2(2x2).
2. Find the derivative of y = sec2 2x.
3. Find the derivative of 3 cot(x + y) = cos y2.
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