Question

Y=e^2x+2x производная

Answer 1

e^(2x)`=2*e^(2x)

2x`=2

(e^(2x)+2x)`=e^(2x)`+2x`=2e^2x+2

.............................................

Answer 2

$y=e^{2x}+2x;\\ y'=\left(e^{2x}+2x\right)'=\left(e^{2x}\right)'+\left(2x\right)'=\\ =e^{2x}\cdot\left(2x\right)'+2=2e^{2x}+2=2\left(e^{2x}+1)$

Answer 3

To find the derivative of the given function Y = e^(2x) + 2x, we'll use the rules of differentiation. The derivative of e^(u) with respect to x is e^(u) times the derivative of u with respect to x.

So, applying the rules:

1. Derivative of e^(2x) with respect to x: d/dx [e^(2x)] = e^(2x) * d/dx [2x] = e^(2x) * 2 = 2e^(2x)

2. Derivative of 2x with respect to x: d/dx [2x] = 2

Now, adding the derivatives together:

d/dx [e^(2x) + 2x] = 2e^(2x) + 2

So, the derivative of the function Y = e^(2x) + 2x is 2e^(2x) + 2.