Find the derivative of f(x). f(x) = xe^x f′(x) = ______

Identify Functions: First, identify the two functions that are being multiplied in f(x) = xe^x. The first function is x and the second function is e^x. Find Derivative of x: Next, find the derivative of the first function, which is x. The derivative of x with respect to x is 1. Find Derivative of e^x: Then, find the derivative of the second function, which is e^x. The derivative of e^x with respect to x is e^x itself. Apply Product Rule: Now, apply the product rule for differentiation. The product rule states that the derivative of a 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. So, f′(x) = (1)(e^x) + (x)(e^x). Simplify Expression: Simplify the expression obtained in the previous step. f′(x) = e^x + xe^x.

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Find the derivative of $f(x)$ . $\newline$ $f(x) = x e^x$ $\newline$ $f'\left(x\right) =$ ______

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Calculus

Find derivatives using the product rule I

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Q. Find the derivative of

f(x)

\newline

f(x) = x e^x

\newline

f'\left(x\right) =

______

Identify Functions: First, identify the two functions that are being multiplied in $f(x) = xe^x$ . The first function is $x$ and the second function is $e^x$ .
Find Derivative of $x$ : Next, find the derivative of the first function, which is $x$ . The derivative of $x$ with respect to $x$ is $1$ .
Find Derivative of $e^x$ : Then, find the derivative of the second function, which is $e^x$ . The derivative of $e^x$ with respect to $x$ is $e^x$ itself.
Apply Product Rule: Now, apply the product rule for differentiation. The product rule states that the derivative of a 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. So, $f'(x) = (1)(e^x) + (x)(e^x)$ .
Simplify Expression: Simplify the expression obtained in the previous step. $f'(x) = e^x + xe^x$ .