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## Homework Statement

Calculate the taylor polynom of order 3 at (0,0,0) of the function with well-known series (that means I can't just take the derivatives)

[tex]f(x,y,z)=\sqrt{e^{-x}+\sin y+z^{2}}[/tex]

## Homework Equations

## The Attempt at a Solution

I wrote the functions within the square root as taylor polynomials and got

[tex]f(x,y,z)=\sqrt{1+-x+\frac{1}{2}x^{2}-\frac{1}{6}x^{3}+y-\frac{1}{6}y^{3}+z^{2}}[/tex]

But then I don't really know how to "remove" the square root. I already tried to just plug the term inside the square root in the taylor expansion of [tex]\sqrt{1+x}[/tex] but that didn't really work out very well.