Partial Derivatives of a and b

[Liquidxlax]

Homework Statement

m=a+b n=a²+b²

find partials (dm/db)_a and (db/dm)_n

The Attempt at a Solution

(dm/db)_a = 1 is that right?

and

(db/dm)_n I'm not sure how to get all the variables into one equation but

a = sqrt(b²-n)

so

m = b - sqrt(b²-n)

can someone help out please?

 

[cepheid]

Homework Statement

m=a+b n=a²+b²

Wait, so are you saying that m = a + bn AND m = a² + b²?

 

[Liquidxlax]

Wait, so are you saying that m = a + bn AND m = a² + b²?

no

m=a+b and n=a^2 +b^2

 

[cepheid]

no

m=a+b and n=a^2 +b^2

Okay.

(dm/db)_a = 1 is that right?

Yeah.

and

(db/dm)_n

This suggests that you want the function b(n,m), so you have to take what you have

m = b - sqrt(b²-n)

solve it for b, and then differentiate that w.r.t. m, keeping n constant.

 

[Liquidxlax]

Okay.



Yeah.




This suggests that you want the function b(n,m), so you have to take what you have



solve it for b, and then differentiate that w.r.t. m, keeping n constant.

well i came here to late, i did try to do it the way you stated, but I'm not sure if i did it right. I could have done it by implicit differentiation or w.e it is called, which i did do. So we shall see whether i got it or not.