Question

Compute for the derivative of the function below for x = 1. f(x)=2xex

Answer 1

Answer:

$[\frac{dy}{dx}]_{x=1} =4e$

Solution:

Differentiate given function with respect to x

let

$y = 2x {e}^{x} \\ \\ \frac{dy}{dx} = 2x \frac{d {e}^{x} }{dx} + 2 {e}^{x} \frac{dx}{dx} \\ \\ = 2x {e}^{x} + 2 {e}^{x} \\ \\ \frac{dy}{dx} = 2 {e}^{x} (x + 1)$
Now to find derivative at x= 1,put the value x= 1 in above equation

$[\frac{dy}{dx}]_{x=1}= 2 {e}^{1} (1 + 1) \\ \\ = 4e$
Hope it helps you.