Calculate the frist order differential of the function f(x,y) = x^{4}*y^{2}+2*x-y^{7}+3Attached is an example of how to do this sec (from lecture). f(x,y)= x*y2 3f : R→ IRf: IR"→ IRS2 c IRMn= 21a = (2,,a2 ) e IR?%3D1f"(@) e £ (R* , & (R", *")) = L (R° R" ; IR")nL ( IR?, d (IR°, IR) ) = L (R², IR²IR: IR→d (IR, IR)f"(a) : R*x R?pl2),IR(2)f"(a.) ((k,h),(huhe) =6xy?1°dy dx学」6xy6x*yhexeflag)= x°y?2xy38y = 3 x'yax2036 a, o60,2²202+ hz (k, 6,q + h, ba*0,20. k k2 + 60,0 kih, + 60,. hikaQ2

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Calculate the frist order differential of the function f(x,y) = x^{4}*y^{2}+2*x-y^{7}+3

Calculate the frist order differential of the function f(x,y) = x^{4}y^{2}+2x-y^{7}+3

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Calculate the frist order differential of the function f(x,y) = x^{4}*y^{2}+2*x-y^{7}+3

Attached is an example of how to do this sec (from lecture).

f(x,y)
= x*y
2 3
f : R→ IR
f: IR"→ IR
S2 c IRM
n= 2
1
a = (2,,a2 ) e IR?
%3D
1
f"(@) e £ (R* , & (R", *")) = L (R° R" ; IR")
n
L ( IR?, d (IR°, IR) ) = L (R², IR²
IR
: IR
→d (IR, IR)
f"(a) : R*x R?
pl2),
IR
(2)
f"(a.) ((k,h),
(huhe) =
6xy?
1°
dy dx
学」
6xy
6x*y
hexe
flag)= x°y?
2xy3
8y = 3 x'y
ax
20
3
6 a, o
60,2²
202
+ hz (k, 6,q + h, ba*0,
20. k k2 + 60,0 kih, + 60,. hika
Q2

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