# Partial derivative

teng125
f( x(1), ......, x(n) ) = sum (i=1) sin(x(i)^2) x(i)

does anybody knows how to solve this pls

d_leet
teng125 said:
f( x(1), ......, x(n) ) = sum (i=1) sin(x(i)^2) x(i)

does anybody knows how to solve this pls

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

Homework Helper
Gold Member
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.

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??

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

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??

Homework Helper
Gold Member
Dearly Missed
It isn't an equation, it is a definition of the function f.

teng125
okok......thanx

Homework Helper
Gold Member
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)

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

Homework Helper
Gold Member
Dearly Missed
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)

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