You are Here: Home >< Maths

C3 help? ^-^ watch

1. Given that
x=sec²y+tany
Show that
dy/dx = cos²y/(2tany+1)

I know it's an easy question and I would be able to do it if it started y=... but it's confusing me =(
2. Just use the result that dy/dx is one over dx/dy. Then it's a standard differentiation (albeit with the usual letters swapped) followed by a flip.
3. you have to use implicit differentiation:

x=sec2y+tany
1=2(sec(y))(sec(y)(tan(Y))dy/dx + sec2y(dy/dx)
1=2(sec2y)(tany)dy/dx + sec2y(dy/dx)
1=(dy/dx)[(sec2y) + (2tany + 1)

Thus dy/dx = cos2y/(2tany+1)

Alternatively, you can just do dx/dy and then inverse what you get.
4. Thanks heaps both of you ^-^

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: November 25, 2005
Today on TSR

University open days

Wed, 21 Nov '18
• Buckinghamshire New University
Wed, 21 Nov '18
• Heriot-Watt University
Wed, 21 Nov '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

Chat with other maths applicants