# How do you calculate the derivative of the function #f(x)=e^x(x^2 + 1)#?

The answer is:

This is because the rule says:

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To calculate the derivative of the function f(x) = e^x(x^2 + 1), you can use the product rule of differentiation, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.

Applying the product rule to f(x), we get:

f'(x) = (e^x)(x^2 + 1) + e^x(2x)

Simplifying this expression gives the derivative of f(x):

f'(x) = e^x(x^2 + 1) + 2xe^x

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