Differentiation of Summation operators

**salohcin** · January 15th 2011, 11:30 AM

Hello all,

I am having a hard time understanding how to differentiate summation operators. More specifically, I was given the following solution that I do not understand. Any step by step advice (or a link) would be fantastic....

$\dfrac{d}{dx}$$\sum\nolimits_{i}p_{i}x_{i}=p_{i}$ I do not understand why this is equal to p, not the sum of p

Thank you kindly for the help,

Nick

**chisigma** · January 15th 2011, 11:47 AM

May be that the formula is...

$\displaystyle \frac{d}{d x_{i}} \sum_{i} p_{i}\ x_{i} = p_{i}$ (1)

... and if the $x_{i}$ are independent variables that's true...

Kind regards

$\chi$ $\sigma$

**pickslides** · January 15th 2011, 11:48 AM

What if $\dfrac{d}{dx_i}$$\sum\nolimits_{i}p_{i}x_{i}=p_{i}$ ?

**HallsofIvy** · January 15th 2011, 02:22 PM

Originally Posted by salohcin

Hello all,

I am having a hard time understanding how to differentiate summation operators. More specifically, I was given the following solution that I do not understand. Any step by step advice (or a link) would be fantastic....

$\dfrac{d}{dx}$$\sum\nolimits_{i}p_{i}x_{i}=p_{i}$

As the others are implying, what you have written makes no sense. The sum depends on many different variables, labeled $x_1$ , $x_2$ , ..., $x_n$ but you are differentiating with respect to "x" which is not any of the variables!

What you have is something like $\frac{d(p_1y+ p_2z)}{dx}$ where you are differentiating a function of y and z with respect to "x". That derivative is, in fact, 0!

But the partial derivatives of $\frac{\partial (p_1x_1+ p_2x_2+ p_3x_3)}{\partial x_1}= p_1$ , $\frac{\partial (p_1x_1+ p_2x_2+ p_3x_3)}{\partial x_2}= p_2$ , and $\frac{\partial (p_1x_1+ p_2x_2+ p_3x_3)}{\partial x_3}= p_3$

I do not understand why this is equal to p, not the sum of p

Thank you kindly for the help,

Nick

Thread: Differentiation of Summation operators

LinkBack

Thread Tools

Display

Differentiation of Summation operators

Similar Math Help Forum Discussions

Inverse operators

Operators

Example of operators

Second order LDE operators

Compact operators

Search Tags