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Let z = f(z,y) = 2e" ad =<1,1>. Dzf(1,3) =?...

Question

Let z = f(z,y) = 2e" ad =<1,1>. Dzf(1,3) =?

Let z = f(z,y) = 2e" ad =<1,1>. Dzf(1,3) =?



Answers

$$z=x e^{x / y^{2}}$$

You were asked to find the second order Partial derivatives with respect all variables of dysfunction here. So it's to respect to x first you can read it. Uh, but substituting rz end fine two X y squared, taking a first rate of have fine two x minus Y squared two x fine. Three co sign, uh, two x minus y squared. And, uh, me better now I think the second derivative. So we'll have to coastline two x y negative Who? No problem. Plus to co sign two x minus Y squared minus two x fine. Should be for so we have minus for a sign of two x minus y squared. Nothing non minus because derivative of coast I'm negative sign. This is a four because taking a derivative of this inner peace two x minus y with respect to X Amy means the driven that would be just too. So the two in the front multiplied by to actually be before X, and there's no minus y squared because we treat with a constant. So this is our answer. The first problem. Just part of problems. Second part parcels. The respective wives whereto our function, you know to Why were so the first thing you do will be managed to Why Coastline two x weird. Our second diverted will be minus two x Kirsten tiene kind of two x minus y squared minus two y x Find two x minus Y squared times are negative to Why what you write this two x most y squared plus y squared x fine of two. That's most this here on this year, either our answers.

Okay, This equation has three variables Z squared equals x squared plus y squared. So, we had to be given extra information. DX DT is two. Dy DT is three. Find DZ DT when X is five and y is 12. All right. So every one of these is changing with respect to T. So when you take the derivative of the square, you get to Z times the derivative Ozzy, which is DZ DT equals two X times the derivative of X. Dx DT plus two Y times the derivative of Y Dy DT. So we can divide the twos off of all of them. Okay? So find DZ DT when X is five, Ny is 12. So five is gonna go here. 12 is gonna go here but we don't have anything for the Z. So we have to stop and find that first. Use the original equation. So, Z squared equals five squared last 12 squared. That's 25 plus 1 44. That's 1 69. So, Z is plus minus The square root of 169, which is 13. That's where he's positive 13 1st. So 13 DZ DT equals five times two plus 12 times three. So DZ DT equals 10 plus 36. 46/13. Okay, And then when you plug in uh minus 13 for Z, you'll get dizzy. D T Equals -46/13

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