Evaluate the partial derivatives fx(x,y) and fy(x,y) at the given point (x0,y0). Note that (x0 and y0 the zeros are below like down exponentials). f(x,y)=(x-5y)^2+(8y-8x)^2+5; at (8,-8)...

Evaluate the partial derivatives fx(x,y) and fy(x,y) at the given point (x0,y0).

Note that (x0 and y0 the zeros are below like down exponentials).

f(x,y)=(x-5y)^2+(8y-8x)^2+5; at (8,-8)

fx(8,-8)=
fy(8,-8)=

Asked on by mavimalik

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pramodpandey | College Teacher | (Level 3) Valedictorian

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`f(x,y)=(x-5y)^2+(8y-8x)^2+5`

differentiate f with respect to x and y partially ,we have

`f_x(x,y)=2(x-5y) d(x-5y)+2(8y-8x) d(8y-8x) `

`f_x(x,y)=2(x-5y) (1)+2(8y-8x) (-8)`

`f_x(x,y)=2(x-5y)-16(8y-8x)`

`f_x(8,-8)=2(8+5xx8)-16(-8xx8-8xx8)`

`f_x(8,-8)=2(8+40)-16(-64-64)`

`fx(8,-8)=96+16xx128=2144`

`f_y(x,y)=2(x-5y) d(x-5y)+2(8y-8x) d(8y-8x)`

`f_y(x,y)=2(x-5y) (-5)+2(8y-8x)(8)`

`f_y(x,y)=-10(x-5y)+16(8y-8x) `

`f_y(8,-8)=-10(8+5xx8)+16(-8xx8-8xx8)`

`f_y(8,-8)=-10(8+40)+16(-128)`

`f_y(8,-8)=-480-2048=-2528`

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