x Turn on thread page Beta
 You are Here: Home >< Maths

# partial differentiation watch

1. x = r sin A cos B, y = r sin A sin B, z = r cos A.

Find (∂x/∂r), treating x as a function of (A,B,r), and (∂r/∂x)
treating r as a function of x,y,z.

i got the first part ∂x/∂r=sinAcosB

how do i treat r as a function of x,y,z?
x = r sin A cos B, y = r sin A sin B, z = r cos A.

Find (∂x/∂r), treating x as a function of (A,B,r), and (∂r/∂x)
treating r as a function of x,y,z.

i got the first part ∂x/∂r=sinAcosB

how do i treat r as a function of x,y,z?
Indeed,

This is spherical polar coordinates, where we know that

To prove this, open the spoiler:

Spoiler:
Show

Thus, the simplest way to do this would to use this equation;

Where r is a function of (x,y,z), r(x,y,z).

Also, just a note, the general form of spherical polar co-ordinates is , not .

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: December 26, 2014
Today on TSR

### 'All unis should close except Oxbridge & RG'

What do you think?

### Should I fight a topless girl for my BF?

Discussions on TSR

• Latest
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

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE