What is the derivative of y=x^2*e^x
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x^2*e^x
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To find the derivative of the function y = x^2 * e^x, we can use the product rule and the chain rule.
The product rule states that if we have two functions u(x) and v(x), their derivative w.r.t x (denoted as u'(x) and v'(x) respectively) is given by:
(d/dx)(u(x) * v(x)) = u(x) * v'(x) + v(x) * u'(x)
In this case, u(x) = x^2 and v(x) = e^x.
So, using the product rule, we have:
y'(x) = (d/dx)(x^2 * e^x)
Using the product rule, we get:
y'(x) = x^2 * (d/dx)(e^x) + e^x * (d/dx)(x^2)
Now, let's find the derivative of each term individually:
(d/dx)(e^x) = e^x (since the derivative of e^x is equal to e^x)
(d/dx)(x^2) = 2x (since the derivative of x^2 is equal to 2x)
Substituting these derivatives back into the equation, we have:
y'(x) = x^2 * e^x + e^x * 2x
Simplifying further:
y'(x) = e^x * (x^2 + 2x)
Therefore, the derivative of y = x^2 * e^x is y'(x) = e^x * (x^2 + 2x).