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:

math expression

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:

math expression

 

Example 1:

Find the derivative of s = sec(3t + 2).


Answer

You can change the function in this LiveMath document.

LIVEMath

 

Example 2:

Find the derivative of x = θ3 csc 2θ.

Answer

 

Example 3:

Find the derivative of y = sec43x.

Answer


Exercises

1. Find the derivative of y = csc2(2x2).

 

Answer


2. Find the derivative of y = sec2 2x.

Answer


3. Find the derivative of 3 cot(x + y) = cos y2.

Answer




Didn't find what you are looking for on this page? Try search:

The IntMath Newsletter

Sign up for the free IntMath Newsletter. Get math study tips, information, news and updates each fortnight. Join thousands of satisfied students, teachers and parents!

Given name: * required

Family name:

email: * required

See the Interactive Mathematics spam guarantee.

Calculus Lessons on DVD

get MathTutorDVDs

Easy to understand calculus lessons on DVD. See samples before you commit.

More info: Calculus videos

 

Book mark this page

Add this page to Del.icio.us, Furl, Digg, StumbleUpon, Google, whatever...

 


Need a break? Play a math game. Well, they all involve math... No, really!

dumbolf memoTST bola shadow factory mindfields trick-hoops-challenge crystal clear