Question

) Find the partial derivative indicated. Assume the variables are restricted to a domain on which the function is defined. d/dx (x^2e^(sqrt(2xy))

Answer 1

@Brostep0s

Answer 2

this is what i got x^2(e^(sqrt(2x))/(sqrt2x))+2xe^(sqrt(2xy))

Answer 3

is that supposed to be d/dx times the rest?

Answer 4

no its the derivative with respect to x i think

Answer 5

I think:
\[\frac{ \delta }{ \delta x }x ^{2}e \sqrt{2xy}=\]
\[=xe ^{\sqrt{2xy}}\left( 2+\frac{ x ^{2}y }{ \sqrt{2xy} } \right)\]

Answer 6

sorry \[x ^{2}e ^{\sqrt{2xy}}\]

Answer 7

that didnt work out

Answer 8

its assuming y is a constant i think, because it is the partial derivative

Answer 9

and:
\[\frac{ \delta }{ \delta y }x ^{2}e ^{\sqrt{2xy}}=\frac{ x ^{3} }{ \sqrt{2xy} }e ^{\sqrt{2xy}}\]

Answer 10

I know that y is like a constant, please note that when you derive the function sqrt(2xy) you will get:
\[\frac{ y }{ \sqrt{2xy} }\]

Answer 11

d/dx with respect to x of sqrt(2xy)=2/(2(sqrt2))

Answer 12

@myininaya i need your veteran expertise

Answer 13

@pmkat14 are you sure? and y where is, if you said it was a constant, then y will remain

Answer 14

oops where is y

Answer 15

oh shoot your right

Answer 16

so then it wouuld be x^2e^(y/sqrt(2xy))+(2xe^(sqrt(2xy))) ?

Answer 17

please, you say \[\frac{ \delta }{ \delta x }\]?

Answer 18

\[2xe^\sqrt{2xy}+e ^{y/\sqrt{2xy}}x^2\]

Answer 19

please , I have made an error before so I'm very sorry.
Now your first term is right! the second one it is no right!,
because the exponent of e^(...) can not change

Answer 20

\[\frac{ y }{ \sqrt{2xy} }\]
is the derivative of the exponent, which is a factor not an exponent!

Answer 21

isnt the derivative of e^(any ecponent) ln(e)e^(original exponenet)
where ln(e)=1

Answer 22

sorry, if you have to calculate the derivative of a function namely:
\[f(x,y)=e ^{g(x,y)}\]
then the derivative of f with respect to x is:
\[e ^{g(x,y)}*\frac{ \delta g }{ \delta x }\]
are you agree?

Answer 23

yes

Answer 24

then, please apply that above to calculate the second term

Answer 25

please note that in your case we have:
\[g(x,y)=\sqrt{2xy}\]
referring to the example above

Answer 26

\[\partial\]

\partial