# Thread: how do you take this partial derivative

1. ## how do you take this partial derivative

(x1^p+x2^p)^1/p

2. Originally Posted by s0urgrapes
(x1^p+x2^p)^1/p
is this expression correct?

$\displaystyle (x_1^p + x_2^p)^{\frac{1}{p}}$

if so, w/respect to which variable will you take the partial derivative?

3. Originally Posted by skeeter
is this expression correct?

$\displaystyle (x_1^p + x_2^p)^{\frac{1}{p}}$

if so, w/respect to which variable will you take the partial derivative?
yes it is correct and with respect to x1 and x2

4. do u have to expand it to derive it easier? how do u expand that?

5. Originally Posted by s0urgrapes
do u have to expand it to derive it easier? how do u expand that?
no, do not expand. use the chain rule. do you know how?

6. Originally Posted by Jhevon
no, do not expand. use the chain rule. do you know how?
it doenst work out to what i need to do in the question if i use the chain rule.. i have no idea what to do

7. Originally Posted by s0urgrapes
it doenst work out to what i need to do in the question if i use the chain rule.. i have no idea what to do
ok, lets think of a simpler example. say you had $\displaystyle (x^5 + 4)^4$, and you wanted to differentiate that with respect to $\displaystyle x$. how would you do it?

do the same thing here. when you want to find the derivative with respect to $\displaystyle x_1$, say, just imagine that everything else is a constant, and differentiate as you normally would

8. Originally Posted by Jhevon
ok, lets think of a simpler example. say you had $\displaystyle (x^5 + 4)^4$, and you wanted to differentiate that with respect to $\displaystyle x$. how would you do it?

do the same thing here. when you want to find the derivative with respect to $\displaystyle x_1$, say, just imagine that everything else is a constant, and differentiate as you normally would
thats different because 4 is a normal number
idk what to do when its to the power of 1/p...

9. Originally Posted by s0urgrapes
thats different because 4 is a normal number
idk what to do when its to the power of 1/p...
fine. lets say "4" was "y" in the same question. so we want to differentiate $\displaystyle (x^5 + 4)^y$ with respect to $\displaystyle x$. just follow the rules. the power rule says, bring the power down, multiply, and subtract one from the power as long as it's a constant. so do that. the derivative is

$\displaystyle y(x^5 + 4)^{y - 1} \cdot 5x^4$

see? can you apply this to what you are doing?

10. Originally Posted by Jhevon
fine. lets say "4" was "y" in the same question. so we want to differentiate $\displaystyle (x^5 + 4)^y$ with respect to $\displaystyle x$. just follow the rules. the power rule says, bring the power down, multiply, and subtract one from the power as long as it's a constant. so do that. the derivative is

$\displaystyle y(x^5 + 4)^{y - 1} \cdot 5x^4$

see? can you apply this to what you are doing?
is there lns anywhere? dont u need ln when u take a power of a variable?

11. Originally Posted by s0urgrapes
is there lns anywhere? dont u need ln when u take a power of a variable?
the power is NOT a variable! that's what i'm trying to get across to you. when taking partial derivatives, EVERY variable but the variable you are differentiating with respect to is treated as a constant. here i was differentiating with respect to "x", so "y" was treated as a constant, because it is not "x"

maybe "y" was a bad letter to use, because it is usually used to mean "a function of x". that is not how it is meant here. it is just some other variable that is treated as a constant when differentiating with respect to x

so now can you try the problem to make sure you get it