Derivadas parciales Mating-1

Sea la función

 $F(x,y)=x^2y^2−2xy^2$  
Determine el valor de  $\frac{\partial F}{\partial x}$  como  $\frac{\partial F}{\partial y}$  en el punto  $P\left(2,1\right)$  

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   $\frac{\partial F}{\partial x}=2$   $\frac{\partial F}{\partial y}=0$  

•  $\frac{\partial F}{\partial x}=2$   $\frac{\partial F}{\partial y}=2$  

•  $\frac{\partial F}{\partial x}=0$   $\frac{\partial F}{\partial y}=0$  

•  $\frac{\partial F}{\partial x}=0$   $\frac{\partial F}{\partial y}=2$  

Sea la función

 $\theta(r,s)=\sqrt{r^2+s^2}+\frac{r}{s}$  
Determine el valor de  $\frac{\partial\theta}{\partial r}$  como  $\frac{\partial\theta}{\partial s}$  en el punto  $P\left(3,4\right)$  

•  $\frac{\partial\theta}{\partial r}=\frac{27}{20}$   $\frac{\partial\theta}{\partial s}=\frac{49}{80}$ 
  

•  $\frac{\partial\theta}{\partial r}=\frac{17}{20}$   $\frac{\partial\theta}{\partial s}=\frac{39}{80}$ 

•  $\frac{\partial\theta}{\partial r}=\frac{17}{20}$   $\frac{\partial\theta}{\partial s}=\frac{49}{80}$ 

•  $\frac{\partial\theta}{\partial r}=\frac{31}{20}$   $\frac{\partial\theta}{\partial s}=\frac{49}{80}$ 

Sea la función

 $F\left(x,y\right)=3x^3y-2x^2y^2+y^3$  
Determine el valor de  $\frac{\partial F}{\partial x}$  como  $\frac{\partial F}{\partial y}$  en el punto  $P\left(1,-2\right)$  

•  $\frac{\partial F}{\partial x}=-34$   $\frac{\partial F}{\partial y}=23$ 
  

•  $\frac{\partial F}{\partial x}=34$   $\frac{\partial F}{\partial y}=-23$ 

•  $\frac{\partial F}{\partial x}=-34$   $\frac{\partial F}{\partial y}=-23$ 

•  $\frac{\partial F}{\partial x}=34$   $\frac{\partial F}{\partial y}=23$ 

Sea la función

 $F\left(x,y\right)=\ln(1+2x^2+3y^2)$  
Determine el valor de  $\frac{\partial F}{\partial x}$  como  $\frac{\partial F}{\partial y}$  en el punto  $P\left(1,2\right)$  

•  $\frac{\partial F}{\partial x}=-\frac{4}{15}$   $\frac{\partial F}{\partial y}=-\frac{4}{5}$ 
  

•  $\frac{\partial F}{\partial x}=\frac{4}{15}$   $\frac{\partial F}{\partial y}=-\frac{4}{5}$ 

•  $\frac{\partial F}{\partial x}=\frac{4}{15}$   $\frac{\partial F}{\partial y}=\frac{4}{5}$ 

•  $\frac{\partial F}{\partial x}=\frac{4}{5}$   $\frac{\partial F}{\partial y}=\frac{4}{15}$ 

Sea la función

 $F\left(x,y\right)=e^{-x}(2y^2−x^2)$  
Determine el valor de  $\frac{\partial F}{\partial x}$  como  $\frac{\partial F}{\partial y}$  en el punto  $P\left(1,2\right)$  

•  $\frac{\partial F}{\partial x}=1.019978389$   $\frac{\partial F}{\partial y}=-1.839397205$ 
  

•  $\frac{\partial F}{\partial x}=1.839397205$   $\frac{\partial F}{\partial y}=1.019978389$ 

•  $\frac{\partial F}{\partial x}=-1.839397205$   $\frac{\partial F}{\partial y}=1.019978389$ 

•  $\frac{\partial F}{\partial x}=1.019978389$   $\frac{\partial F}{\partial y}=1.839397205$ 

Dada la función z = f(x,y) en forma implícita, hallar ∂z/∂y.

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• Es otra expresión.

Obtener

 $\frac{\partial F}{\partial x}$  de la función  $F=\left(z^2+1\right)^x$  

•  $\left(z^2+1\right)^x\ln\left(z^2+1\right)$  

•  $\left(z^2+1\right)^x\ln\left(z^2+1\right)x$  
  

•  $\left(z^2+1\right)^x\ln\left(x\right)$  

•  $x\left(z^2+1\right)^{x-1}\left(2z\right)$  

Obtener

 $\frac{\partial F}{\partial y}$  de la función  $F=sen\left(xy\right)\cos\left(xy\right)$  

•  $x\cos^2\left(xy\right)-x\ \sin^2\left(xy\right)$  

•  $y\cos^2\left(xy\right)-y\ \sin^2\left(xy\right)$  
  

•  $x\cos\left(xy\right)\sin\left(xy\right)-y\ \sin\left(xy\right)\cos\left(xy\right)$  

•  $x\cos^2\left(xy\right)-\ \sin^2\left(xy\right)$  

Obtener

 $\frac{\partial F}{\partial y}$  de la función  $F=y^{\sin\left(xz\right)}$  

•  $y^{\sin\left(xz\right)}\cos\left(xy\right)\ln\left(yz\right)$  

•  $\sin\left(xz\right)y^{\left\{\sin\left(xz\right)-1\right\}}$  
  

•  $y^{\sin\left(xz\right)}\cos\left(xz\right)\ln\left(yx\right)$  

•  $y^{\sin\left(xz\right)}\cos\left(z\right)$  

Obtener

 $\frac{\partial F}{\partial x}$  de la función  $F=\ln\left(\frac{x+y}{z}\right)$  

•  $\frac{z-x-y}{z^2}$  

•  $\frac{-1}{z}\left(x+y\right)$  
  

•  $\frac{z}{x+y}$  

•  $\frac{1}{x+y}$