Question

Differentiate: f(x) = e^2x

Answer 1

Given:

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

Aim:

We need to differentiate the function f(x).

Step-by-step explanation:

Differentiate the function f(x).

`(df\mleft(x\mright))/(dx)=(de^(2x))/(dx)`
`\text{Use chain rule }(de^(2x))/(dx)=^{}e^(2x)\frac{d(2x)^{}}{dx}\text{.}`

`f^(\prime)(x)=e^(2x)\cdot(d(2x))/(dx)`

`\text{Use chain rule }\frac{d(2x)^{}}{dx}=2.`

`f^(\prime)(x)=e^(2x)\cdot2`

`f^(\prime)(x)=2e^(2x)`

Final answer:

`f^(\prime)(x)=2e^(2x)`