Is the following true or false? d/dx[x^3e^x]=x^2e^x (3x+2)

1 answer:

3 0

It's false. It's a product so...
Derivative of the first TIMES the second PLUS derivative of second TIMES the first.

Derivative of the first (x^3) = 3x^2
Times the second = 3x^2 * e^x

Derivative of the second = e^x (remains unchanged)
Times the first = e^x * x^3
So the answer would be (3x^2)(e^x) + (e^x)(x^3)
which can be factorised to form x^2·e^x(3 + x)

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<h3>How to determine the ratio?</h3>

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Dawn : Mandy = 6 : 7

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Multiply the second ratio by 3.5.

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Mandy : Belle = 2 * 3.5 : 3 * 3.5

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Mandy : Belle = 7 : 10.5

Mandy's ratios in both equation are the same.

So, we have:

Dawn : Mandy : Belle = 6 : 7 : 10.5

Remove Mandy's ratio

Dawn : Belle = 6 : 10.5

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Hence, the ratio of Dawn to Belle's savings is 4 : 7