Question

derivada de f(x,y) = cos²x+y²
(derivada parcial de duas variáveis)

Answer 1

Para a derivada parcial de x consideramos o y uma constante, ou seja, ele vai zerar e o reciproco para a derivada parcial de y:

$\frac{\delta f(x,y)}{\delta x}=-2\cos(x)\sin(x)=-\sin(2x)\\\\\frac{\delta f(x,y)}{\delta y}=2y$

Answer 2

$\large\boxed{\begin{array}{l}\rm\dfrac{\partial}{\partial x}(cos^2(x)+y^2)=2cos(x)\cdot -sen(x)\\\\\rm\dfrac{\partial}{\partial x}(cos^2(x)+y^2)=-2sen(2x)\end{array}}$

$\large\boxed{\begin{array}{l}\rm\dfrac{\partial}{\partial y}(cos^2(x)+y^2)=2y\end{array}}$