Assignment 17 Query

course Mth 271

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16:53:12

2.5.2 inner, outer fns for (x^2-3x+3)^3

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RESPONSE -->

u = x^2-2x+3

y = u^3

confidence assessment: 3

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16:53:15

The first function you evaluate is x^2 - 3x + 3.

You then cube this result.

So the breakdown to get f(g(x)) form is

f(z) = z^3

g(x) = x^2 - 3x + 3. **

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RESPONSE -->

self critique assessment: 3

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16:53:24

2.5.8 inner, outer fns for (x+1)^-.5

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RESPONSE -->

u = x+1

y = u^-.5

confidence assessment: 3

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16:53:27

The first function you evaluate is x+1.

You then take this result to the -5 power.

So the breakdown to get f(g(x)) form is

f(z) = z^-.5

g(x) = x+1. **

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RESPONSE -->

self critique assessment: 3

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16:53:36

2.5.24 der of f(t) = (9t+2)^(2/3) by gen power rule

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RESPONSE -->

dy/dx = 2/3(9t+2)^-1/3 (9)

= 18(9t+2)^-1/3/3

= 6(9t+2)^-1/3

confidence assessment: 3

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16:53:38

This function is of the form u^(2/3), where u = 9 t + 2.

The derivative of f(t) = u^p is f ' (t) = p * u^(p-1) * u ', by the general power rule.

Here p = 2/3, and u ' = (9t + 2)' = 9 so we have

f ' (t) = p u^(p-1) * u ' = 2/3 * u^(2/3 - 1) * 9 = 6 * u^(-1/3), or since u = 9 t + 2

f ' (t) = 6 ( 9 t + 2)^(-1/3). **

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RESPONSE -->

self critique assessment: 3

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16:53:48

2.5.32 der of f(x) = (25+x^2)^(-1/2) by gen power rule

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RESPONSE -->

dy/dx = -1/2(25+x^2)-3/2*(2x)

= -x(25+x^2)^-3/2

confidence assessment: 3

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16:53:51

Using inner function u = 25+x^2 and outer function = (u)^(-1/2) we get

n u^(n-1) du/dx is -1/2 * u^(-3/2) * 2x = - x ( 25+x^2)^(-3/2). **

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RESPONSE -->

self critique assessment: 3

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Your work looks very good. Let me know if you have any questions. &#