Funktionen:
\[\frac{\left(1-x^2\right) \left(y^2-4\right)-x^2-y^2+5}{\left(x^2+y^2+1\right)^2}\]

Partiell derivata map x:
\[\frac{-2 x \left(y^2-4\right)-2 x}{\left(x^2+y^2+1\right)^2}-\frac{4 x \left(\left(1-x^2\right) \left(y^2-4\right)-x^2-y^2+5\right)}{\left(x^2+y^2+1\right)^3}\]

Partiell derivata map y:
\[\frac{2 \left(1-x^2\right) y-2 y}{\left(x^2+y^2+1\right)^2}-\frac{4 y \left(\left(1-x^2\right) \left(y^2-4\right)-x^2-y^2+5\right)}{\left(x^2+y^2+1\right)^3}\]

😊

fina formler .(JavaScript must be enabled to view this email address)

Denna labbdel är godkänd!

mvh 😊

\[\frac{\left(1-x^2\right) \left(y^2-4\right)-x^2-y^2+5}{\left(x^2+y^2+1\right)^2}\]

Partiell derivata m.a.p. x :

\[\frac{-2 x \left(y^2-4\right)-2 x}{\left(x^2+y^2+1\right)^2}-\frac{4 x \left(\left(1-x^2\right)
\left(y^2-4\right)-x^2-y^2+5\right)}{\left(x^2+y^2+1\right)^3}\]

Partiell derivata m.a.p. y :

\[\frac{2 \left(1-x^2\right) y-2 y}{\left(x^2+y^2+1\right)^2}-\frac{4 y \left(\left(1-x^2\right)
\left(y^2-4\right)-x^2-y^2+5\right)}{\left(x^2+y^2+1\right)^3}\]

Fina formler ys!!

Här kommer funktionen och dess partialderivator på LaTeX-format från mig!

Funktionen:
\[\frac {\left (1 - x^2 \right)\left (y^2 - 4 \right) - x^2 - y^2 +
5} {\left (x^2 + y^2 + 1 \right)^2}\]

Partialderivata m.a.p. x:
\[\frac{-2 x \left(y^2-4\right)-2 x}{\left(x^2+y^2+1\right)^2}-\frac{4 x \left(\left(1-x^2\right) \left(y^2-4\right)-x^2-y^2+5\right)}{\left(x^2+y^2+1\right)^3}\]

Partialderivata m.a.p. y:
\[\frac{2 \left(1-x^2\right) y-2 y}{\left(x^2+y^2+1\right)^2}-\frac{4 y \left(\left(1-x^2\right) \left(y^2-4\right)-x^2-y^2+5\right)}{\left(x^2+y^2+1\right)^3}\]

@ jonathan

Formlerna ser snygga och fina ut!

Du är godkänd på detta labbmoment!

mvh 😊

Function:

\[\frac{\left(1-x^2\right) \left(y^2-4\right)-x^2-y^2+5}{\left(x^2+y^2+1\right)^2}\]

Derivata map x

\[\frac{-2 x \left(y^2-4\right)-2 x}{\left(x^2+y^2+1\right)^2}-\frac{4 x
\left(\left(1-x^2\right)
\left(y^2-4\right)-x^2-y^2+5\right)}{\left(x^2+y^2+1\right)^3}\]

Derivata map y

\[\frac{2 \left(1-x^2\right) y-2 y}{\left(x^2+y^2+1\right)^2}-\frac{4 y
\left(\left(1-x^2\right)
\left(y^2-4\right)-x^2-y^2+5\right)}{\left(x^2+y^2+1\right)^3}\]

@MBerger
fina formler
Du är godkänd på denna labbuppgift!

mvh 😊