Question

F`(x)=2хe^x найти производную, помогите , пожалуйста

Answer 1

2*e^x+2*x*e^x



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Answer 2

Calculation of the Derivative of F(x)

To find the derivative of the function F(x) = 2xe^x, we can use the rules of differentiation. The derivative of a function represents the rate at which the function is changing with respect to its independent variable.

The derivative of F(x) can be calculated using the product rule and the chain rule. The product rule states that if we have two functions u(x) and v(x), then the derivative of their product is given by (u(x)v'(x) + v(x)u'(x)). The chain rule states that if we have a composite function f(g(x)), then the derivative of the composite function is given by (f'(g(x)) * g'(x)).

Let's calculate the derivative of F(x) step by step:

1. Apply the product rule: - Let u(x) = 2x and v(x) = e^x. - Calculate u'(x) and v'(x). - u'(x) = 2 - v'(x) = e^x - Apply the product rule: F'(x) = u(x)v'(x) + v(x)u'(x).

2. Substitute the values: - F'(x) = (2x)(e^x) + (e^x)(2) - Simplify: F'(x) = 2xe^x + 2e^x

Therefore, the derivative of F(x) = 2xe^x is F'(x) = 2xe^x + 2e^x.

Please let me know if you need any further assistance!