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Q:
Why does the Product Rule State the Value as the Product of the Absolutes?
I’m asking this question because I’m quite unsure of the significance behind this formula, would someone be able to shed some light?
$\frac{d}{dt}(x^3) = 3x^2\frac{dx}{dt}$
I saw this formula and I found it strange, because I would have assumed that the integral solution would be $x^3(t) = x^3(0) + \int_{0}^{t} 3x^2 dt$. Instead I see that the final answer is the product of the absolute value of the function and the function itself, which would have led to the answer $x^3(t) = x^3(0)$
A:
The usual integral form is the product of the two functions:
$$ x^3(t)= x^3(0)\,e^{3t} \;. $$
super(Function.newForNumber(Integer.MIN_VALUE, 0, Integer.MAX_VALUE, Integer.MIN_VALUE), 1,
Integer.MIN_VALUE, 0, -1, 0);
}
/* (non-Javadoc)
* @see org.eclipse.collections.api.block.procedure.primitive.Tuple2#t2_5()
*/
@Override
public T2 t2_5()
{
return new T2(2, 1);
}
/* (non-Javadoc)
* @see org.eclipse.collections.api.block.procedure.primitive.Tuple2#t2_6()
*/
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