You are Here: Home >< Maths

# Differentiate the following with respect to x watch

1. sin^2 (x) / cos^3 (x)

Erm...
2. have you come across the quotient rule?

let and
3. Quotient rule? Or write as and then either use an identity connecting tan and sec or use the product rule.
4. ye i've tried to use thazt method. but i get:

2cos^4 (x) sin (x) + 3cos^2 (x) sin^3 (x)
________________________________ ____________

cos^6 (X)
5. Quotient rule

(d/dx)f(x)/g(x)=
[f'(x)g(x)-g'(x)f(x)]/(g(x)^2)

Sorry but I suck with LaTex, so if that just looks a mess, look on wikipedia or something for the quotient rule, it's right what they've got written for it.
6. i fully understand the quotient rule..tbh is my answer correct? just not simplified enough??
7. (Original post by FoOtYdUdE)
ye i've tried to use thazt method. but i get:

2cos^4 (x) sin (x) + 3cos^2 (x) sin^3 (x)
________________________________ ____________

cos^4 (X)
(b) Cancel out what you can, then take a common factor of the top and remember sin^2+cos^2 =1.

sinx(2+sin^2 x)
_______________
cos^4 x
9. soz, it was cos^6 x not cos^4 x (denominator)
10. (Original post by DFranklin)
(b) Cancel out what you can, then take a common factor of the top and remember sin^2+cos^2 =1.
erm..
11. (Original post by FoOtYdUdE)
erm..
As uninformative posts go, this scores pretty highly.

What is the problem?
12. (Original post by DFranklin)
As uninformative posts go, this scores pretty highly.

What is the problem?
13. This is my working:

Is it coreect? Have I gone wrong anywhere??

(2cosxsinx.cos^3 x - (-3cos^3 x sinx . sin^2 x) ) / ( cos^3 x)^2 )

= (2 cos^4 x sinx + 3cos^2 x sin^3 x ) / (cos^6 x)
14. (Original post by FoOtYdUdE)
This is my working:

Is it coreect? Have I gone wrong anywhere??

(2cosxsinx.cos^3 x - (-3cos^3 x sinx . sin^2 x) ) / ( cos^3 x)^2 )

= (2 cos^4 x sinx + 3cos^2 x sin^3 x ) / (cos^6 x)
Thats fine, just cancel down. Take out common factors, and remember that sin^2 x + cos^2 x = 1
15. As has already been said above, you should really try and simplify expressions before you differentiate them.

Read up to see how this expression goes to tan^2xsecx
Which can be found using the product rule.

Or it cancels even further to (sec^2x - 1)secx = sec^3x - secx
Which can be found using the chain rule.

So, would you rather use the chain rule, the product rule, or the quotient rule?

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: February 7, 2010
The home of Results and Clearing

### 3,523

people online now

### 1,567,000

students helped last year
Today on TSR

### IT'S TODAY!

A-level results chat here

### University open days

1. Bournemouth University
Fri, 17 Aug '18
2. University of Bolton
Fri, 17 Aug '18
3. Bishop Grosseteste University
Fri, 17 Aug '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams