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n.a.s.h
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Homework Statement
what is the derivative of e^[(-X^2-2x+1)/2]
Homework Equations
The Attempt at a Solution
Is this right?
= -(x+1)e^[(-x²-2x+1)]
n.a.s.h said:Homework Statement
what is the derivative of e^[(-X^2-2x+1)/2]
Homework Equations
The Attempt at a Solution
Is this right?
= -(x+1)e^[(-x²-2x+1)]
The derivative of e^x is simply e^x itself. This is because the derivative of any exponential function is equal to the function itself.
To find the derivative of e^x, you can use the power rule. This means that you bring down the exponent and subtract 1 from it. So for e^x, the derivative would be e^x.
The derivative of e^x is important because it is the rate of change of the function e^x at any given point. It also has many real-world applications, such as in finance and growth models.
One example of using the derivative of e^x is in population growth models. If we have a population that is growing exponentially at a rate of e^x, the derivative of this function would give us the rate of growth at any given time.
No, the derivative and integral of e^x are not the same. The integral of e^x is e^x + C, where C is a constant, while the derivative is simply e^x. They are inverse operations of each other, but not equivalent.