MTH231

$$g_x\left(x,y\right)=e^{xy^2}\left(1+x^2y\right)$$

$$g_x\left(x,y\right)=e^{xy^2}\left(1+xy^2\right)$$

$$g_x\left(x,y\right)=xy^2e^{xy^2}$$

$$g_x\left(x,y\right)=xe^{xy^2}$$

$$g_x\left(x,y\right)=2x^2ye^{xy^2}$$

The domain is all (x,y) such that $$x^2+y^2=9$$

The domain is the set of all points $$\left(x,y\right)$$ for which $$x^2+y^2\ge0$$

The domain is the circular disk of radius 3 with center at the origin

The domain is the set of all points $$\left(x,y\right)$$ for which $$x^2+y^2\ge9$$

NOTA

10

7

8

0

DNE

NOTA

$$6xe^{5y}-4y\sin\ 2x$$

$$6xe^{5y}+4y\cos\ 2x$$

$$6yxe^{5y}+4x\sin\ 2x$$

$$3x^2e^{5y}+2y\cos\ 2x$$

NOTA

NOTA

$$\frac{\partial w}{\partial t}=\frac{\partial w}{\partial x}\frac{\partial x}{\partial p}\frac{\partial p}{\partial t}+\frac{\partial w}{\partial y}\frac{\partial y}{\partial p}\frac{\partial p}{\partial t}$$

$$\frac{\partial w}{\partial t}=\frac{\partial w}{\partial x}\frac{\partial x}{\partial s}\frac{\partial s}{\partial t}+\frac{\partial w}{\partial y}\frac{\partial y}{\partial p}\frac{\partial p}{\partial t}$$

$$\frac{\partial w}{\partial t}=\frac{\partial w}{\partial x}\frac{\partial x}{\partial p}\frac{\text{d}p}{\text{d}t}+\frac{\partial w}{\partial y}\frac{\partial y}{\partial p}\frac{\text{d}p}{\text{d}t}$$

$$\frac{\partial w}{\partial t}=\frac{\partial w}{\partial x}\frac{\partial x}{\partial q}\frac{\partial q}{\partial u}\frac{\partial u}{\partial t}+\frac{\partial w}{\partial y}\frac{\partial y}{\partial v}\frac{\partial v}{\partial s}\frac{\partial s}{\partial t}$$

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NOTA