Free Printable derivadas parciales

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)

a)

\frac{\partial F}{\partial x}=2

\frac{\partial F}{\partial y}=0

b)

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

c)

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

d)

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

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)

a)

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

b)

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

c)

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

d)

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

3.

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)

a)

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

b)

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

c)

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

d)

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

4.

Sea la función

F\left(x,y\right)=\ln\left(x^2+y\right)

Determine el valor de

\frac{\partial F}{\partial x}

como

\frac{\partial F}{\partial y}

en el punto

P\left(1,2\right)

a)

$\frac{\partial F}{\partial x}=\frac{2}{3}$ $\frac{\partial F}{\partial y}=\frac{1}{3}$

b)

$\frac{\partial F}{\partial x}=\frac{3}{2}$ $\frac{\partial F}{\partial y}=\frac{1}{3}$

c)

$\frac{\partial F}{\partial x}=\frac{1}{3}$ $\frac{\partial F}{\partial y}=\frac{2}{3}$

d)

$\frac{\partial F}{\partial x}=\frac{1}{3}$ $\frac{\partial F}{\partial y}=\frac{3}{2}$

5.

Sea la función

F\left(x,y\right)=e^{-\frac{\left(x^2+y^2\right)}{3}}

Determine el valor de

\frac{\partial F}{\partial x}

como

\frac{\partial F}{\partial y}

en el punto

P\left(1,2\right)

a)

$\frac{\partial F}{\partial x}=-0.1259170685$ $\frac{\partial F}{\partial y}=-0.2518341371$

b)

$\frac{\partial F}{\partial x}=-0.1259170685$ $\frac{\partial F}{\partial y}=0.2518341371$

c)

$\frac{\partial F}{\partial x}=-0.2518341371$ $\frac{\partial F}{\partial y}=-0.1259170685$

d)

$\frac{\partial F}{\partial x}=0.2518341371$ $\frac{\partial F}{\partial y}=0.1259170685$

6.

Sea la función

F\left(x,y\right)=(3x+y)Cos(xy)

Determine el valor de

\frac{\partial F}{\partial x}

como

\frac{\partial F}{\partial y}

en el punto

P\left(1,2\right)

a)

$\frac{\partial F}{\partial x}=4.962633970$ $\frac{\partial F}{\partial y}=10.34141477$

b)

$\frac{\partial F}{\partial x}=10.34141477$ $\frac{\partial F}{\partial y}=4.962633970$

c)

$\frac{\partial F}{\partial x}=-4.962633970$ $\frac{\partial F}{\partial y}=-10.34141477$

d)

$\frac{\partial F}{\partial x}=-10.34141477$ $\frac{\partial F}{\partial y}=-4.962633970$

7.

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)

a)

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

b)

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

c)

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

d)

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

8.

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)

a)

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

b)

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

c)

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

d)

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

derivadas parciales

Total questions: 8

Worksheet time: 32mins

Similar Resources on Wayground