Question

What is the derivative of `e^(2x)`?

Answer 1

differentiate by parts

Explanation:

Derivative of `e^x=e^x` (always)
then
`dy/dx=e^(2x)`
now multiply the derivative of `2x` with`e^(2x)`
`dy/dx=2x`
=`(n)*x^(n-1)*2`
the final answer
`e^(2x)*2`

Answer 2

`2e^(2x)`

Explanation:

Given: `d/dx(e^(2x))`.

Let `y=e^(2x)`.

Use the chain rule, which states that,

`dy/dx=dy/(du)*(du)/dx`

Let `u=2x,:.(du)/dx=2`.

Then, `y=e^u,:.dy/(du)=e^u`.

Combining, we get:

`dy/dx=e^u*2`

`=2e^u`

Substituting back `u=2x`, we get the final answer:

`color(blue)(barul(|=2e^(2x)|)`