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il63 [147K]
2 years ago
6

Differentiating Exponential Functions In Exercise, find the derivative of the function. y = x2ex

Mathematics
1 answer:
I am Lyosha [343]2 years ago
8 0

Answer:

y' = xe^{x}(2 + x)

Step-by-step explanation:

If we have a product function y, in the following format

y = f(x)*g(x)

This function has the following derivative

y' = f'(x)*g(x) + g'(x)*f(x)

In this problem, we have that:

y = x^{2}e^{x}

So

f(x) = x^{2}, f'(x) = 2x, g(x) = e^{x}, g'(x) = e^{x}

The derivative of the function is:

y' = f'(x)*g(x) + g'(x)*f(x)

y' = 2xe^{x} + x^{2}e^{x}

y' = e^{x}(2x + x^{2})

y' = xe^{x}(2 + x)

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