F(X,Y,Z)

[CatchThis2]

Let f(x,y,z)= x^2-2y^2 / y^2+2z^2 Then

fx(x,y,z)=

fy(x,y,z)=

fz(x,y,z)=

 

[galactus]

Let \(\displaystyle f(x,y,z)= \frac{x^{2}-2y^{2}}{ y^{2}+2z^{2}}\)

They want you to find the partial derivatives w.r.t the respective variables x, y, z.

\(\displaystyle f_{x}(x,y,z)=\)

Hold y and z constant and differentiate w.r.t x:

\(\displaystyle f_{x}=\frac{2x}{y^{2}+2z^{2}}\)

See?. The denominator is a constant for this one and we only have to differentiate x^2 in the numerator because 2y^2 is a constant and becomes 0. Using the quotient rule we have:

\(\displaystyle \frac{(y^{2}+2z^{2})(2x)-(x^{2}-2y^{2})(0)}{(y^{2}+2z^{2})^{2}}=\frac{2x}{y^{2}+2z^{2}}\)

Now, try the other two.

 

[CatchThis2]

To differentiate for y I should get

(0^2)-(2z^2)(2x)-(x^2-2(0)^2)(0)/y^2+2z^2 ?

 

[galactus]

Please refrain from insults. There is no need for undue hostility.