1. ## Differentiate fractions

Hi

How would you differentiate the following:

2x^2 + 2000/r

I know it would be first 4x + ?UNKNOWN?

Im not sure how to differenctiate 2000/r

2. Originally Posted by taurus
Hi

How would you differentiate the following:

2x^2 + 2000/r

I know it would be first 4x + ?UNKNOWN?

Im not sure how to differenctiate 2000/r
Hello,

that depends:

a) If your function reads $f(x) = 2x^2 + \frac{2000}{r}$ then r is considered to be a constant.

b) If your function reads $f(r) = 2x^2 + \frac{2000}{r}$ then x is considered to be a constant.

c) If your function reads $f(t) = 2x^2 + \frac{2000}{r}$ then x and r are considered to be a constant.

According to your rematk it seems to be a)

3. oh right, could you run through how you would solve each of those then please for my own knowledge?

4. Originally Posted by earboth
Hello,

that depends:

a) If your function reads $f(x) = 2x^2 + \frac{2000}{r}$ then r is considered to be a constant.

b) If your function reads $f(r) = 2x^2 + \frac{2000}{r}$ then x is considered to be a constant.

c) If your function reads $f(t) = 2x^2 + \frac{2000}{r}$ then x and r are considered to be a constant.

According to your rematk it seems to be a)
Yes.

Or, if it is in a case where r is also a variable, and the differentiation is with respect to x, then
d/dx 2000/r
= d/dx 2000*r^(-1)
= 2000*[-1*r^(-2)*dr/dx]
= -[2000/(r^2)](dr/dx)