- #1
T.Engineer
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find the 1st and 2nd derivative of the following equation
-2z*e^-(z^2)
step by step.
Thanks alot!
-2z*e^-(z^2)
step by step.
Thanks alot!
radou said:Any ideas on this one? if this is a function of z, and you're differentiating with respect to z, does the product rule sound familiar?
T.Engineer said:it is -2Z (-2z)e^-(z^2) --- [e^-(z^2)*(-2)]
CompuChip said:Yep, that's the way to go.
But are you sure about that minus sign?
Can you quote the product rule?
The 1st derivative is a measure of how a function changes at a specific point. It represents the slope or rate of change of the function at that point.
The 1st derivative is calculated by taking the limit of the difference quotient as the change in the input variable approaches zero. This can also be written as the derivative of the function f(x) with respect to x or f'(x).
The 1st derivative tells us about the direction and steepness of the function at a specific point. A positive 1st derivative indicates an increasing function, while a negative 1st derivative indicates a decreasing function. The magnitude of the 1st derivative also gives us information about the rate of change of the function.
The 2nd derivative is a measure of how the 1st derivative changes at a specific point. It represents the concavity or curvature of the function at that point.
The 2nd derivative is the derivative of the 1st derivative. In other words, it is the rate of change of the slope or rate of change of the function. A positive 2nd derivative indicates a function that is concave up, while a negative 2nd derivative indicates a function that is concave down. The 2nd derivative can also help us identify points of inflection in a function.