Differentiate TU= 4 sqr x1 + x2

[feelgooddan]

TU= 4 sqr x₁ + x₂

differentiate by _x1 if x₁=9 and x₂=8

 

[Hobse]

First of all, if you actually plug those numbers in there at this particular moment and then differentiate, you're going to end up with an answer of zero, so you shouldn't do that.

Differentiating anything with a sqrt should go something like this:

Firstly, move the sqrt into an exponent form.

sqrt( x ) = x^(1/2)

Now, take the derivative with respect to x (x1 in your case), using the power rule.

d/dx (x^(1/2)) = (1/2)x^(-1/2) = 1 / [2*(sqrt(x))]

If it applies, which I don't believe it does in your example, don't forget the chain rule.

Hope that helps.

 

[feelgooddan]

First of all, if you actually plug those numbers in there at this particular moment and then differentiate, you're going to end up with an answer of zero, so you shouldn't do that.

Differentiating anything with a sqrt should go something like this:

Firstly, move the sqrt into an exponent form.

sqrt( x ) = x^(1/2)

Now, take the derivative with respect to x (x1 in your case), using the power rule.

d/dx (x^(1/2)) = (1/2)x^(-1/2) = 1 / [2*(sqrt(x))]

If it applies, which I don't believe it does in your example, don't forget the chain rule.
Hope that helps.

Thank you! But I guess you forgot 4, is not it? So, the answer going to be 2 / (sqrt(x1))

I'm really interested in x₂ here. So, it is going to be 0 in differentiation, right?

 

[Fooze]

I believe the point was to just give you an idea of how it would go, not do the exact problem for you.

However, yes... x2 is 0 since it's treated as a constant.