Free Printable Derivadas parciales Mating-1

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(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)

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

5.

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)

$\frac{\partial F}{\partial x}=2.940335529$ $\frac{\partial F}{\partial y}=-3.310914971$

b)

$\frac{\partial F}{\partial x}=3.310914971$ $\frac{\partial F}{\partial y}=2.940335529$

c)

$\frac{\partial F}{\partial x}=-3.310914971$ $\frac{\partial F}{\partial y}=2.940335529$

d)

$\frac{\partial F}{\partial x}=2.940335529$ $\frac{\partial F}{\partial y}=3.310914971$

6.

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

a)

b)

c)

d)

e)

Es otra expresión.

7.

Obtener

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

de la función

F=\left(z^2+1\right)^x

a)

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

b)

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

c)

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

d)

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

8.

Obtener

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

de la función

F=sen\left(xy\right)\cos\left(xy\right)

a)

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

b)

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

c)

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

d)

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

9.

Obtener

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

de la función

F=y^{\sin\left(xz\right)}

a)

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

b)

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

c)

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

d)

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

10.

Obtener

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

de la función

F=\ln\left(\frac{x+y}{z}\right)

a)

$\frac{z-x-y}{z^2}$

b)

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

c)

$\frac{z}{x+y}$

d)

$\frac{1}{x+y}$

Derivadas parciales Mating-1

Total questions: 10

Worksheet time: 3hrs 30mins

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