# Partial derivative

1. Jul 15, 2006

### teng125

f( x(1), ......, x(n) ) = sum (i=1) sin(x(i)^2) x(i)

does anybody knows how to solve this pls

2. Jul 15, 2006

### d_leet

What is this exactly? And what does this have to do with partial derivatives?

3. Jul 15, 2006

### quasar987

Don't be intimidated by the sum sign. Write what the sum is explicitely and you'll find a more familiar form. Also, you can resolve the special case n=3 and renaming x(1)=1, x(2)=y and x(3)=z first before tackling the more abstract general case of n variables.

4. Jul 16, 2006

### teng125

f( x(1), ......, x(n) ) = sin(x(1)^2) x(1) + sin(x(2)^2)x(2) + sin(x(2)^2)x(2) + sin(x(3)^2)x(3) + ...... +sin(x(n)^2)x(n)

should i write this eqn like this??

5. Jul 16, 2006

### arildno

There's nothing here to "solve".
You just have a function f, given by the prescription:
$$f(x_{1},\cdots{x}_{n})=\sum_{i=1}^{n}x_{i}\sin(x_{i}^{2})$$

6. Jul 16, 2006

### teng125

so u mean i just have to write the eqn above and no need to do partial derivative as the question ask to do so??

7. Jul 16, 2006

### arildno

It isn't an equation, it is a definition of the function f.

8. Jul 16, 2006

### teng125

okok......thanx

9. Jul 16, 2006

### quasar987

Now that you've expanded the sum, it should be easier to see what the derivative wrt x(1) is. (remember, the derivative of a sum is the sum of the derivative)

10. Jul 16, 2006

### teng125

f( x(1), ......, x(n) ) = sin(x(1)^2) x(1) + sin(x(2)^2)x(2) + sin(x(2)^2)x(2) + sin(x(3)^2)x(3) + ...... +sin(x(n)^2)x(n)

so should i write this eqn like this??

for quasar987

11. Jul 16, 2006

### arildno

Again, this isn't an equation, but a definition of a function
Secondly, try to formulate IN YOUR OWN WORDS what you are supposed to do with this function! (This, you have failed to do so far)

12. Jul 16, 2006

### Gagle The Terrible

This form of the expression makes it easier to "find" the derivatives, so I would write the equation this way.

13. Jul 16, 2006

### quasar987

Can you find the derivative of f(x) = xsin(x²) ?

14. Jul 16, 2006

### teng125

i think can by using u'v + vu' formula rite??

15. Jul 16, 2006

### VietDao29

No, no, no. Another wrong answer. It's uv'. Repeat after me: (uv)' = u'v + uv', (uv)' = u'v + uv'.