transcribe the solution in digital format please wehave.в (x,y,z) = 40%, у-4z + 40хвузz3-20nz2To Find gradient if possible,possibleHere f(x,y,z) is a scalor function hence it isto find gradient, by applying vector operatorfunctiontoScalor(zifixe7fA>=afi+af tax33,аж (4oxy'z+ 40x³y³z3-20xz2);+ 24 (4oxyt+(дох уч-сложуayчохвуз: z3-20xrза счоху + 402 уво+чох-чодеждіг) = [соў + 12oxy?z3-2oz2] i +[-160xy5z +120xyz'jy120x3y32+40x2th2x06-+ [40xy=4+[иоху

Answered: wire have. To Find gradient if…

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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transcribe the solution in digital format please

we
have.
в (x,y,z) = 40%, у-4z + 40хвузz3-20nz2
To Find gradient if possible,
possible
Here f(x,y,z) is a scalor function hence it is
to find gradient, by applying vector operator
function
to
Scalor
(zifixe7fA>
=
afi+
af t
ax
33,
аж (4oxy'z+ 40x³y³z3-20xz2);+ 24 (4oxyt+
(дох у
ч-
сложу
ay
чохвуз: z3-20xr
за счоху + 402 у
во
+
чох
-ч
одеждіг) = [соў + 12oxy?z3-2oz2] i +[-160xy5z +120xyz'jy
120x3y32+40x2
th
2x06-
+ [40xy=4+
[иоху

Expert Solution

Step 1: Function f(x,y,z)

We have $f left parenthesis x comma y comma z right parenthesis equals 40 x y to the power of negative 4 end exponent z plus 40 x cubed y cubed z cubed minus 20 x z to the power of negative 2 end exponent$

We have to find the gradient if possible,

Here f(x,y,z) is a scalar function hence it is possible to find gradient.

So, by applying vector operator to scalar function:

Gradient of f= $nabla f left parenthesis x comma y comma z right parenthesis equals fraction numerator partial differential f over denominator partial differential x end fraction i plus fraction numerator partial differential f over denominator partial differential y end fraction j plus fraction numerator partial differential f over denominator partial differential z end fraction k$