Question

Qual a derivada de f(x,y)=(3-x^2-y^2)^1/2 ?

Answer 1

Boa Noite!!
Derivadas Parciais.

$f(x) = (3-x^2-y^2)^{ \frac{1}{2}}$

$f(x)= \frac{1}{2}(3-x^2-y^2)^\frac{-1}{2} *2x$

$f(x) = x (3-x^2-y^2)^\frac{-1}{2}$

$\boxed{ f(x) = \frac{x}{ \sqrt{(3-x^2-y^2)} } }$

$f(y)= (3-x^2-y^2)^ \frac{1}{2}$

$f(y) = \frac{1}{2} (3-x^2-y^2)^ \frac{-1}{2} * 2y$

$f(y) = y (3-x^2-y^2)^\frac{-1}{2}$

$\boxed{ f(y)= \frac{y}{ \sqrt{(3-x^2-y^2)} } }$

Espero ter ajudado.
Abraço!