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4 years ago

Use the distributive property to expand: x^-3 y^0(x^2-3x^5 y^4)

1 answer:

4 0

${x}^{ - 3} {y}^{0} ( {x}^{2} - 3 {x}^{5} {y}^{4} ) \\ = {x}^{ - 3} (1) ( {x}^{2} - 3 {x}^{5} {y}^{4} ) \\ = {x}^{ - 1} - 3 {x}^{2} {y}^{4}$

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3 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

2 points) Suppose w=xy+yzw=xy+yz, where x=et, y=2+sin(t)x=et, y=2+sin⁡(t), and z=2+cos(3t)z=2+cos⁡(3t). A ) Use the chain rule t

Olenka [21]

Answer:

$\frac{\partial w}{\partial t} = y(e^t) +(x+z)*(cos(t)) - 3y*sin(3t)$

Step-by-step explanation:

First, note that

$\frac{\partial x}{\partial t} = e^{t} \\\frac{\partial y}{\partial t} = cos(t)\\$

And using the chain rule in one variable

$\frac{\partial z}{\partial t} = -3sin(3t)$

Now remember that the chain rule in several variables sates that

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

Therefore the chain rule in several variables would look like this.

$\frac{\partial w}{\partial t} = y(e^t) +(x+z)*(cos(t)) - 3y*sin(3t)$

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4 years ago

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