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Problem 9

Integration and Differentiation In Exercises 5 and 6 verify the statement by showing that the derivative of the right side equals the integrand on the left side.

$\frac{d y}{d x}=x^{3 / 2}$

Answer

$$

y=\frac{2}{5} x^{5 / 2}+C

$$

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## Discussion

## Video Transcript

all right in this question, they're actually asking us, Um, they have B y over DX on walls X to the three halves, and they want us thio kind of reverse engineer and say, What was the original function at the derivative? Equal three halves. So let's think backwards. When we take the derivative, we subtract one, so we have to add one. So we know that our function here, what have equal X to the five halves and we don't have a coefficient of X so are five abs. When multiplied by the coefficient, would give us one. Well, that would be the reciprocal. And let's see, if I add tend to the back, Would that change anything? So let's see. Does this work? When I take the derivative five halves times to Fitz gives me one s and I subtract, I get three cabs and the 10 balls away. So now let's make it a little bit more generic, and we're going to say that why equals X to the five calves, the 10 balls away. Just because it's a concert, I'm just gonna represent that with a C because it could be any number can 12 1 200

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