Question

encontre as derivadas parcias de primeira ordem da função f(x,y)=xcosy

Answer 1

$f\left(x,\,y \right )=x\cos y$


$\bullet\;\;\dfrac{\partial f}{\partial x}=\dfrac{\partial}{\partial x}\left(x \cos y \right )\\ \\ \dfrac{\partial f}{\partial x}=\cos y \cdot \dfrac{\partial}{\partial x}\left(x \right )\\ \\ \dfrac{\partial f}{\partial x}=\cos y \cdot 1\\ \\ \boxed{\dfrac{\partial f}{\partial x}=\cos y}$


$\bullet\;\;\dfrac{\partial f}{\partial y}=\dfrac{\partial}{\partial y}\left(x \cos y \right )\\ \\ \dfrac{\partial f}{\partial y}=x \cdot \dfrac{\partial}{\partial y}\left(\cos y \right )\\ \\ \dfrac{\partial f}{\partial y}=x \cdot \left(-\mathrm{sen\,}y \right )\\ \\ \boxed{\dfrac{\partial f}{\partial y}=-x \mathrm{\,sen\,}y}$