Have worked through to get some sort of answer, but find the evaluation (simplest bit) impossible - wood for trees, I think.(adsbygoogle = window.adsbygoogle || []).push({});

given d2(e^(xy^2)/dy^2 I need to evaluate for x=2, y=0

now using chain rule d(e^(xy^2))/dy = d(e^u)/du du/dy

where u=xy^2 & d(e^u)/du = e^u

=> x(2y) e^(xy^2)

fine for 1st order

moving on

d(x(2y) e^(xy^2))/dy

removing constants

2x(d(ye^(xy^2))/dy

use product rule

d(uv)/dy = v du/dy + u dv/dy

u =e^(xy^2) & v=y

=> 2x(e^(xy^2)(d(y)/dy)+y(d(e^xy^2)))

chain rule again

where u=xy^2 & d(e^u)/du = e^u

2x(ye^(xy^2)(x(d(y^2)/dy)))+e^(xy^2)

which shuld be d2(e^xy^2)/dy2

=> 2x(xy(2y)e^(xy^2)+e^(xy^2)

Now evaluate for x=2, y=0

everything goes to 0 ??????

I'v gone throught he difficult bits in the book, now the simple stumps me!!!

Please help before I bang my head against the wall again!!!

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# Homework Help: Evalute partial diff with values of x&y

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