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andrey2020 [161]

3 years ago

9

I'm not sure where to start and how to differentiate this.

1 answer:

Mazyrski [523]3 years ago

5 0

The picture is not clear. let me assume y = (x^4)ln(x^3)

product rule :
d f(x)g(x) = f(x) dg(x) + g(x) df(x)

dy/dx = (x^4)d[ln(x^3)/dx] + d[(x^4)/dx] ln(x^3)
= (x^4)d[ln(x^3)/dx] + 4(x^3) ln(x^3)

look at d[ln(x^3)/dx]
d[ln(x^3)/dx]
= d[ln(x^3)/dx][d(x^3)/d(x^3)]
= d[ln(x^3)/d(x^3)][d(x^3)/dx]
= [1/(x^3)][3x^2] = 3/x
... chain rule (in detail)

end up with
dy/dx = (x^4)[3/x] + 4(x^3) ln(x^3)
= x^3[3 + 4ln(x^3)]

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QUESTION B.

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$x \le \frac{6}{2}$ .

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Answer: 5. $x \le 3$ , closed dot at 3 and shaded to the left(B).

QUESTION C

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Add 7 to both sides to get;

$x\:>\:-4+7$

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Answer: 7. $x\:>\:3$ , open dot at 3 and shaded to the right.(C)

QUESTION D

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We have

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$\frac{4}{-4}\:>\:x$

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Answer: 6. $x\:$ open dot at -1, and shaded to the left(E)

QUESTION F

The given inequality is $-2x+3\:$

Add -3 to both sides to get;

$-2x\:$

$-2x\:$

Divide both sides of the inequality by -2 and reverse the sign;

$x\:>\:5$

Answer:9. $x\:>\:5$ , open dot at 5 and shaded to the right(F)

QUESTION G

The given inequality is

$5x+1\ge11$

$5x\ge11-1$

$5x\ge10$

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$x\ge2$

Answer ; 10. $x\ge2$ , closed dot at 2 and shaded to the right(G)

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$3x+12\:>\:8x-6$

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$-5x\:>\:-18$

Divide through by -5 and reverse the sign;

$x\:$

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QUESTION I

We have $-3x+4\:$ .

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Expand the bracket to get;

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Group like terms to get;

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